Are you restricted to to a single game piece set?
This might be hugely easier if you can keep state between turn analyses. IE, if a white rook disappears from A5 and some unidentified white piece appears at C5, then it’s probably the rook.
That lack of constraints led us into running face first into issues of generalisation and variability within datasets. As in, exactly what you allude to with limiting the piece sets.
I think in my undergraduate naivety my aspirations were too high with what could reasonably be accomplished. I've spent a lot of time trying to improve an aspect of the project that really didn't need to be improved, which prevented meaningful progress.
Now finals are coming up and I feel terribly stressed. Having trouble functioning. Brain fog, etc. I feel so sad right now.
EDIT: I keep forgetting my password so apparently I have multiple throwaway now. Sorry.
It takes a lot of shortcuts, works with just the right lightning, etc., but worked great as a proof-of-concept :)
We got away with not identifying the pieces by just detecting the color, assuming the game started from the initial position, and assuming only legal moves (the whole game is unambiguous using these assumptions).
It's all old-school computer vision with hand-written features, and I'm pretty confident there is tons of low-hanging fruit, but who has the time.
Set one up at the park and get some insight on those hustled blitz games!