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Kinda important note that was left out:
Up + Select to save state, Down + Select to load state.

This patch over here brings up an interesting scenario for some NES games. Would it be technically possible to save a game almost in the same way as a save state? Maniac Mansion and Crystalis sorta do that, since you can (almost) save anytime, anywhere, and it keeps your exact position and everything. But would that be harder to implement than a normal save that keeps track of fewer variables, and not as accurately?

Yes, you could save a game pretty much like a savestate. CHR RAM is potentially a problem depending on how much you do with it (As the original post mentions). If your game is already using a large portion of the SRAM for its gamestate, that may also present a problem. (Being in SRAM already, it would be saved. But power could be cut between updates of things, so you'd probably want it stored again for the actual save.)

I guess it'd be harder to implement, but it wouldn't be very much harder except for the cases above.