@mwd could we hear an example of your original stereo preset first to see how you are making your stereo image? Once we hear that we'll know if collapsing that image to mono is a good idea or not depending on the arrangement and mix of the song.
If you have stereo effects
after the Cab block within the Axe, and your goal is to have a mix with just one guitar and stereo fx then the best way to record this is to keep all cabs in the Cab block panned centre, then move the Balance knob of that Cab block all the way to the left of say, Output 1. If you want to capture a DI, set your DAW to record the raw guitar signal going into whichever input you're using. Then..send your post Cab effects to a discreet output pair on the Axe Fx (eg Output 2 L and R). You should now have 4 channels to record on 4 tracks..the dry Amp and Cab (Track 1 mono), the raw DI (Track 2 mono), and the post amp stereo fx (Tracks 3 and 4, or as one stereo track). I would take this a step further if we're trying to model reality and also feed the dry amp to a room IR of the main cab, and record that on a 5th track, just like you would record a mono room mic in addition to a close mic in the real world. Now you can pan your dry amp wherever you like in the mix, and then hard pan your stereo fx left and right, or collapse them to mono and then pan that sum to the opposite side of the dry amp etc..
@1234 there seems to be some confusion here regarding source sounds and multitrack recording in general but what you're saying is essentially correct. The confusion here results from the fact that a typical dry Axe Fx preset of just one Amp and Cab block (without any post amp fx and with all the cabs within the Cab block panned centre) is a mono source feeding the left and right outputs of the Axe, which means both channels are identical and recording them both is like duplicating a mono track in the DAW so it isn't necessary. Take many of the factory presets for example, the dry amp and cab isn't panned, but if a stereo reverb or delay etc is active post cab, you now have an image consisting of a dry amp and cab panned centrally, and stereo fx either side, which wouldn't be a very mix friendly image to print because you'd be stuck with the guitar in the middle if you want the full width of the stereo fx, so it's much better to run those fx to a separate output and then to separate tracks in your DAW.
It's all about the desired stereo image. The most basic double tracked guitar sound would be 1 Amp and Cab per take..ie each take is a mono sound and therefore needs to be recorded on a single mono track. A more involved double track guitar sound might be where each take has multiple mics (several close mics and room mics), in which case each take is a multitrack recording, recorded on separate tracks. Once those tracks are recorded per take, you can then choose how to pan them in the mix, but you'd probably hard pan your blend of close mics for take 1 to the left and pan the room mic of take 1 to the right, and then pan your blend of close mics for take 2 hard right and pan the room mic of take 2 to the left.
In the Axe, to mimic all those mics (whether by using multiple cab sounds and amount of room etc), you just need to make sure you route each sound discreetly to it's own output or output pair.
Another scenario would be stereo fx
before two Amp and Cab blocks, with each amp accepting either the left or right signal from those stereo fx, and with each Cab's balance control set hard left or hard right. Again, here you would record those two Amps/Cabs as two separate tracks, and if you wanted you could record those pre fx separately too for reamping later.
So to cut a long story short, don't think about recording the Axe in mono or stereo, think about routing everything to it's own output so you can record it all on separate tracks. Or if you want to commit to a sound when you record it which is often the best idea, work out what your desired image will be and route everything appropriately in the Axe to make that happen.