Create a stereo track in LOGIC using input 1-2 from the Axe. Create a mono track, or two mono tracks, or a stereo track using input 3-4 from the Axe (your unprocessed signal).
Then, you can make the Axe the Output card in Logic Preferences, and on the front panel of the Axe on the In/Out menu change the input from the input jack you usually use, to USB.
Now, the downside, is, you can solo the LOGIC tracks you used to record input 3-4, and it will go through the axe so you can change presets and hear what different amps and cabs would sound like, but you have to SOLO those tracks and not send your entire LOGIC session through the axe, otherwise everything - vocals, drums, keys - everything, will come through and have amp/cab/effects of your guitar.
So, if you solo the dry tracks and play the track while the axe is in USB input mode, you can make a new set of stereo tracks using input 1-2 from the axe and print the re-amped sounds to new tracks.
but while you are doing that process, you can't hear the rest of the instruments in LOGIC. You have to sit through the entire song - unless you punch in for the verse, chorus, or wherever you are re-amping. So, sit through the entire song, while the re-amped track is being recorded, then undo the configuration process - set the axe input back to 1/4" and listen to your newly recorded re-amp track along with the entire LOGIC project and see it if fits in the mix better.
