For what it's worth, I would be very inclined to avoid damaging any existing woodwork.
I'd settle for any deck that fits and can play your vinyl safelyt I'd then place the amp within the cavity [assuming it fits] horizontally or anywhere and live with it for now!
Hook up the speakers and see how it actually sounds. Going for relative perfection at this stage or retro-fitting complex extensions to the amp etc might be an interesting challenge or it could take you on a wild goose chase!
You never know what may turn up that's relatively original or even that you can adapt more successfully/easily. You could put in a lot of work and then not like the sound
Or you could be listening to a Radiogram albeit not quite completed, while researching further!.
Dave W