Can the Axe-Fxs digital I/O run at 44.1 kHz, or any values other than 48 kHz?
No, it’s 48 kHz only. The rationale is that software on a computer could do a better job resampling than a hardware chip. The reason that the native sampling rate is fixed was a hardware design choice. By placing the A/D and D/A clock very close to the converters and using a fixed, dedicated clock you get much better performance since there’s much less clock jitter. As soon as you start putting a clock through logic circuitry and routing it all over the place you introduce jitter and the converter performance degrades.