On the 6504, /IRQ is on pin 3, while the 6507 uses this pin as the RDY input. On the Lisa I/O board, /IRQ is not used and pin 3 is terminated with a pullup resistor. Therefore both 6504 and 6507 will work.
All 650x derivatives use the same chip. On the 28-pin variants, some pins are simply not connected. It would be easy to develop an adapter board that allows the use of a 6502 instead. But who needs something like that? I have made adapter boards for the Z8 (with UB8820M) and for the COP421 (with COP402). These parts have internal ROM and are therefore not so easy to replace, but even those no one has needed yet. They just break very rarely.
I did a quick bit of research and, at least according to the Atari guys there appears to be no reason why you couldn't use a full-blown vintage 6502 in place of a 6507. Things get more interesting by the time we get to the 65C02 (and by extension, the modern WDC parts) - I don't speak 6502 assembly, but according to the Atari guys code that uses illegal opcodes on a vintage 650x will no longer function on the 65C02. Another page I found said that illegal opcodes simply NOP in the 65C02, and some instructions may take an extra cycle or two to complete now.
The I/O ROM for the floppy controller does not use illegal opcodes. So I see no reason why a 65C02 (or 65C04 if there is such a thing) should not work.
You (or the Atari guys) are right -- the CMOS devices replaced the illegal opcodes (which are actually just overlays of two legal opcodes because the instruction decoding is incomplete) with either additional opcodes or NOPs. Unfortunately, there were different implementations of the 65C02 with different sets of additional opcodes. Therefore you have to know exactly which controller type is installed if you want to use them.
http://www.6502.org/tutorials/65c02opcodes.html