I also have a small room, actually 2 small bedrooms. I built myself a tweed deluxe (5e3 with 12” open back cab), bought a small 5w Bugera head w/12” closed back cabinet, and a POD HD when they were $199 on clearance. Nothing is better than cranking an amp up and mic-ing a cabinet. If you can get your Mesa down to 5w, (not using a power soak) and can get your output tubes cranking, I’d try that with a single 12” cab. As another poster said, it would be good to get an open back and a closed back cabinet. The piece of shit Bugera will do 5w without any padding to the output. This enables me to get a good sound that doesn’t sound like the speaker has a blanket over it. I was surprised at how good the Bugera sounds when cranked. I use the 12w tweed for more clean sounds. Neither of the amps are uncomfortably loud and are perfect for recording. I have a 50w Marshall (2203) out in the garage but never use it for recording. It shakes everything in the house.
I use the small adjacent room for electronic drums and amps (kids left home). If I need to record at night I use the POD HD (which is nowhere near as good as your Axe-FX). You may find it convenient to keep the Axe-FX for times when your neighbors are home. My bedroom shares a wall with my “control room” so I have to keep things really low at night to let the wifey sleep.
You’ll get the best results using an amp and mic-ing it, but if I had an Axe-FX, I would keep it. Having as many tools as you can allows for flexibility. I wouldn’t keep all the high powered amps if you don’t play out much. Sell one of them and invest in a low wattage tube amp for recording.