I have also a 1969 Twin reverb, and a Super Sonic 22. I am sure there are other ways around that though but that is what I found works for me. The second way is kind of hard because your guitar sound is so loud it makes it a little difficult to hear the backing track. The first way works pretty well, especially if you're trying to record over a backing track because it is easy to hear both. So what I have been doing ( don't really know if this is the proper way to go about it or not as I am fairly new to recording ) is either using the amplify effect in Audacity to give a negative amplification to the backing track, or more recently, going to the output block on the stomp and boosting the dbs. The only thing I have noticed is that it is hard sometimes to get the level to match the rest of the tracks. I think you will find it really pleasing when you get it to work.
If you haven't got the latest firmware you should get it, I think it's 2.8 - it added a prince of tone / king of tone type pedal that is great, and a few more amp models (I want to say one of them was a tweed bassman and a tweed deluxe - can't remember though). I haven't tried both using stereo effects yet I should do that though that would be great. When I do play it through my amps I have used the 4 cable method to do a 'preamp swap' on the supersonic (as it has an effects loop) or just as effects into either amp. I have recorded quite a bit with it actually. Mostly I play the stomp through headphones as my wife is in medical school - she studies a lot and I try not to disturb her. But since I got the stomp I haven't played them much.