Hi Savaitti, just ripped open the package to the Blueboard and started playing. On one level, it's an impressive piece of gear, but certain decisions (all of which are in the Companion App) are baffling. But anyway...
The Blueboard does not, at this time, have a momentary setting. This makes it a bit hard for us to work with, but anyway...
Regarding your question, you'll note that if you set the Blueboard to Program Change (set the channel to 1) and set up a KNOB to receive from it (a program change knob on channel 1), that'll spin just fine. Now you can have that knob be the supercontrol of any number of buttons (google button groups in midi designer). That's one way to go.
Another way to go is to just use the Blueboard and check it's "thru" option in MIDI Designer. This will send the program changes onward to your Axe-FX.
Does any of this help at all? We're still investigating possibilities, and talking to IK Multimedia to get some changes made (fingers crossed, but it might take a while if it's even possible)...