I think that limiting players to a grid can definitely make the understanding of movement and spatial positioning more obvious.
I have heard that Undead Assault is an FPS that restricts you to grid movement and turning, though I have not experienced it properly myself.
That said, I think it takes something away from the aesthetics of the game. Further, first person shooters and other action games can benefit from the mechanic of precise aiming with the mouse.
Swamp would be a good game for you to try, since it has a free single player mode, and is a first person shooter with some very low vision graphics you can turn off.
A Hero's Call (AHC) would be another interesting one for you to test, though it does not have a free demo.

In Swamp, aiming with the mouse gives the best experience for aiming at zombies and making precise shots.
But the hot keys for turning snap you to face cardinal/ordinal directions so you can quickly orient for navigating.
Moving into a new region speaks the name of that region.
The maps come with built in beacons for the interesting locations, and you can enable one to get a direction and distance announcement, as well as a beeping sound in the direction of the beacon as the crow flies.
There is a configurable radar which plays repeating beep sounds on points near your character, using different sounds to indicate walkable versus wall terrain.
My descriptions will not do any of this justice. You should definitely test the game for yourself.

There is no need to aim in A Hero's Call, so using the mouse is not really important.
That said, it still uses continuous rather than discrete movement and allows you to use the mouse to turn to face any angle.
The hot keys for turning only snap you to cardinal directions.
It uses the same region announcement as Swamp.
It also has a forward speech scan that announces changes in region and blocking terrain in front of you.
I think the automatic forward speech scan is too verbose and detracts significantly from the atmosphere of the game (and I am the one who conceptualized and built that feature), but I still think it is nice to be able to press a key and find out about things in front of you at a distance.
It is a worthwhile feature. I just think the automatic version should be disabled by default to help the game's atmosphere.
It also has a different style of radar than Swamp. Instead of constantly beeping around your character, it only plays beeps to indicate changes in walkable versus wall terrain around you as you move.
Imagine that you have a wall to your left and are moving forward.
Suddenly the space to your left becomes more open as you pass an alley way, so a sound plays to your left to indicate that the left is now more "open".
As you keep moving forward you completely pass the alley way and now have a building to your left, so a different sound plays to your left to indicate that the left is more "closed".
I conceptualized and built that feature because I would sometimes miss a doorway to my left in Swamp because the beeping sound takes time to cover all points and you can easily walk passed a doorway even when you were trying to listen for it.
I think it is a good feature, especially for navigation inside buildings, but may have inadvertantly led to AHC maps being built to be too maze like, as though everywhere is in doors.
AHC also has a beacon system, though it uses path finding to give players precise directions to their destination, rather than a beacon as the crow flies as Swamp does.
When enabled you will hear a voice in the direction you need to travel, saying the name of the cardinal/ordinal direction you need to travel.
Swamp's author intentionally chose the crow flies option because he wanted players to retain the challenge of finding their way around buildings and other obstacles, but to still know the general direction they needed to travel.
We intentionally added the path finding option to AHC to make things as easy as possible for players who have difficulty with first person navigation.
Both games use maps built on grids of terrain tiles, though they use continuous movement.

I agree with Camlorn that most blind gamers who have been blind for several years will be much better at navigating audio environments than sighted players.
We have just had much more practice at it.
That said, I have known gamers who were blind from birth who had very poor spatial reasoning, and as he mentioned, gamers who become blind later in life will have had much less practice.
You can see a similar difference in what practice can do when listening to text to speech (TTS) speeds.
Listen to some TTS on your computer at a speed that is comfortable for you, then listen to some recordings of blind people listening to TTS.
We usually have it at much higher speeds. Speeds that cause most sighted people's initial response to be "You can understand that?"
Though even within the blind community there is a lot of variation. I have heard a recording of Camlorn listening to TTS, and I could definitely not use his speed as my normal day to day speed, yet most sighted people cannot understand the speed I use.

I also agree that sighted developers usually create games that are too simple.
The most common action fighting game for a sighted developer to make is a bop it style game, where your character stands stationary and you hear an enemy in the forward, left, or right directions, and then have to press a key to block or hit them in that direction.
I believe Undead Assault was made by a blind developer, but my guess is that it is grid based because he didn't value aiming with the mouse.
Blind people don't use the mouse in day to day computer usage, and some don't even own a mouse.
Swamp helped introduce a lot of the blind gaming community to the mouse for first person shooters, and it was an uphill battle to get people to switch.

BK3/BD3/Bokurano Daibouken 3 is the best platformer we have, and the game is free, though there is a small fee to purchase the English translation.
ShadowRine/ShadowLine is the best top down old school Legend of Zelda like action RPG we have, but it has no English translation, so you have to use a screen reader addon to play it in machine translated English, and the setup for that is probably more than a sighted developer would be willing to do.
I think Swamp is the best FPS we have, though I did not play Shades of Doom very much.
The Blind Swordsman was made by a sighted developer. It is real time stationary combat, but with continuous turning, and very nice sound, music, and voice acting.
Also see Castaways and SoundRTS for good examples of real time civilization building and real time strategy.

Hope this helps.

Surprised no one has mentioned Code Dungeon yet.

https://stealcase.itch.io/codedungeon

Anyhow, agreed with most of what has been said here. Let your gameplay, not your views on audio navigation, dictate how traversing your world works. The next commercial game I'm working on will be top-down not because of simplicity, but because it's a roguelike-ish thing. But The Last Of Us 2 shows that even complex navigation is at least possible, though I do wish it exposed even more than it does, and think it's a great first effort rather than an ultimate end goal. I'm also mentally prototyping 3-D spaceflight in audio, though I haven't yet knocked together a sandbox to see how practical the ideas actually are.

Thanks for all the input! This is really helpful.

I have played some, and watched quite a few videos of people playing audio games and it's been informative, but sometimes I find it hard to follow what's going on when I'm not aware of the player input. I kind of have to experience it first hand.

About blind players simply being better... Yes, I did miss that at first, but picked up on it when researching audio games. I appreciate that you bring it up because it's an important point. But like I said in my original post, this is a small project. I'm making it for myself first so I can play and appreciate it and learn from it. I don't have any illusions that I'm doing audio game players a service right now.

My possibly unrealistic ambition here is to make a little demo where you can walk around in an environment at your own pace, talk to NPC's and interact with objects. I'd like to be able to hand it someone who has never tried audiogames and while they will probably struggle at first they can play through the experience and focus on the narrative or puzzles and not just the challenge of navigation using spatial audio. I don't want the lack of graphics to feel like a gimmick.

I am definitely taking on board what you're saying about making games for both blind and sighted players rather than trying to make a unified experience that is worse for both. This project will be limited by that exact compromise, but I'm hoping that the experience will make me more equipped to make accessible games in the future, or potentially even collaborate on an audio game with someone blind and experienced with it. But assuming it's even feasible to make a mainstream-friendly audio game, this could just be a distracting rabbit hole and I'd be better served focusing on what I know.

That aside, I have to try out some of the suggested games and process all the great insights before I get a feel for what degrees of freedom and constraints I'd want to experiment with. I have time to consider whether it's a fools errand.

If anyone is curious, I use Unity and I've been learning Audiokinetic's Wwise audio middleware. Unfortunately I'm working a lot right now so I'm mostly just game jamming and tinkering on the side.