I know you don't want to consider iRig Stomp I/O and of course everybody has different needs but to me that's the #1 best choice for live use. AXE I/O is not compatible with iPad anyway so that's not a good choice for iOS devices anyway.
iRig HD 2 is a great single-input unit and you would want to use the AMP OUT with the switch set to FX to get the full effected sound to the board. Note this is a mono output, though, so you may also want to consider using the headphone output to go out to two channels if that is your aim.
If you want MIDI support (for switching, etc) you could look at iRig Pro I/O which is a really great interface for more than guitar and as mentioned would have the MIDI support if that's a requirement.
You can also compare IK mobile interfaces here:
https://www.ikmultimedia.com/products/i ... hp?p=range