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No, it isn't possible for you to have used too many keys. I don't remember there being a chest that I couldn't open in the end either, my guess is you missed one of the broken walls, maybe hiding a chest with a single key?
Your best bet is indeed to retry the floor by selecting a new game.
OK so I restarted and somehow had enough keys to get all the chests and doors open on the first and 2nd floor... I don't know what I did wrong in my first run, but trust me Brandish brothers/sisters, I'm not a liar. Besides the only way I could have "screwed up" was by dropping or selling the 2 keys I needed and I'm just not that dumb.
There's still the matter of B2F still not at 100%. How do you access the large area to the left of the floor? I'm at B4F in my second run now, the "training" floor.
Related question: does beating the game with 100% on all floors unlock anything else than personal satisfaction?