I think the sample rate would make a big difference for
high frequency FM. The higher the sample rate, the fewer aliased frequencies appearing in the audible range. I can't comment on
quantization error or how much difference it would make.
If I were you, I'd forget FM and just go with Phase Modulation instead. Once you start builing complicated FM stuff (multiple carriers/modulators interacting with eachother), it starts to sound like crap (imho), especially with feedback. I can't give a DSP math explanation as to why. Russel Pinkston wrote in the Csound book that complicated FM can introduce DC offset (I can vouch for that) and carrier drift.
Here's an example of 1 carrier, 1 mod PM with feedback: