6510 compatibility only requires adding 6 IO lines mapped to address $1 though (otherwise the 6510 is 6502 compatible enough), so given it's an FPGA based project it wouldn't necessarily be a big ask, and from the webpage it sounds like they're open to suggestions.
I don't think memory at $00 and $01 are the only challenges. The 6510 has a tristateable bus. A regular 6502 doesn't. The C64 used this to disable the 6510 when the Z80 in the cp/m card was active. (I think it also might be used to allow the VIC II to take over the bus as well, but I'm not positive about that.)
Actually the bigger problem with this design on a second read through is that it tries to mirror the ROM and RAM into a 64K on-chip RAM. That won't work on the C64 because of the bank switching and the fact the VICII can access memory everywhere. You'd have to change it to use the on-chip RAM as a smarter cache.
If you were to disable the use of the on-chip RAM it'd be stalled far more than half the time, as it'd be unable to fetch instructions fast enough.
The bank switching uses three of the IO pins, so if you add support for those as I mentioned that fixes both the bank switching and the tape drive (which uses the remaining IO pins).
EDIT: Actually you're right that there's a problem with the bank switching here since it tries to mirror the system RAM/ROM, and it won't be able to as it has only 64K on-chip RAM. You could conceivable get it to work by designating the entire address space as an "IO area" but it'd totally kill performance.
"It may be possible and worthwhile to also support some slightly later machines: The Acorn BBC Micro, Atari 400 and 800, and maybe the Commodore C64 come to mind."
It'll take a more extensive modification than I thought, though, because it does a RAM mirroring thing that is necessary for performance but that kills compatibility with at least the C64.
If you disable the RAM mirroring, all you need to make it compatible is to map the 6 IO pins to address $1. That "solves" the bank switching, but at the cost of killing performance totally as the chip will be starved for memory access most of the time.
Judging from his pictures, he's using a version of the Spartan 6 (XC6SLX9) that has 72KB on-chip RAM, though, so unless he's using any of the RAM for anything else he could still mirror both the 64KB RAM + the KERNAL and BASIC ROMs. But he'd also need to keep track of various VICII registers to know which areas to designate as a "IO areas" to pass through writes for, given the VICII can address memory "everywhere" for sprites, fonts and bitmap data depending on what you write to different registers. Since that can at any time it'd involve a lot of "fun" logic to flush data from the on-chip cache to the C64 memory if a register changes.