You can also use a different method. Rather than use AxeFX modes on your IA's, set them as General Midi. Assign the appropriate CC's for your FX, X/Y etc. You lose the red/green function, instead the lights are off/on which I prefer anyway. In this method, the on/off state of IA's is not "read" from the AxeFX patch, it is controlled by the MFC and stored in the MFC patch.
Here's an example setup, using the 5 preset mode of MFC. In one bank, program all 5 presets to send PC #1, which is your "Super Patch" on the AxeFX. For simplicity, say the chain is OD, Amp (Clean/Dirty via XY), Delay, Chorus, Tremelo and you have the second row of 5 programmed as General Midi IA's for each of these.
Now, the fun part. You get to program the IA's live. Kick Preset 1 switch on MFC. Engage Clean Amp, Delay, Chorus. You see the Edit light blink, stomp that switch. Done, now those IA states are stored in MFC Preset 1 and it will call up your clean/delay/chorus sound. Repeat for preset 2, etc. Once you've done it a few times it's second nature, and easy to program live. You can of course expand this to include as many FX blocks, Amps etc as you can cram into one patch and have IA switches available. The AxeFX stays on the same preset, the MFC has 5 presets that will store various combinations of IA's.