I hadn't seen the work by Paul before. It assumes a lot of capabilities the Apple 1 didn't have; there is no timed interrupt tics and no graphics--not even a proper cursor. :-) You would have to gut a fair amount of its functionality to have something supported by traditional Apple 1 style hardware.
One of my favorite Woz stories about the Apple 1... "I spent a couple of hours trying to get the interrupt version of it working, but I kept failing. I couldn’t write a new program into the PROMs. To do that, I’d have to go to that other building again, just to burn the program into the chip... Finally I gave up and just popped in the other two PROMs, the ones with the 'polling' version of the monitor program. I typed a few keys on the keyboard and I was shocked! The letters were displayed on the screen!"
On MS BASIC, Applesoft v1 and Applesoft v2 were actually both for the Apple 2. There was never a floating point basic from Apple for the Apple 1. There is a (modern) back-ported version around that removes the graphics functions and some of the trig functions. That version can run on just about any 6502 machine with hooks to character in and out routines. I know it has been run on Apple 1 clones. I think it takes around 6.5K of memory.