Have tried swapping out power and output trannies...in a Fender Silverface Champ. Put in a power tranny with more current so I could run 6l6, el34 or 6550 if I wanted to. Tried three different output trannies, and contrary to an earlier opinion, in my experience the output trannies had much more effect than changing out either pre or power tubes or speakers on basic tone and response of the amp...and I am a bit of a GAS tube and speaker guy too. In the case of a Mesa amp, I would not touch the power transformer, but the output tranny is fair game.
Very few guitar players contemplate changing output trannies on their amps. Tubes are much easier, as are speakers. I resonate with Monsta-tone on this thread, nothing is as good as doing the actual experiment. He has done it quite a few times. My hat's off to him, again. Can you do it? Hell yes! Not all that many wires need to be connected for either the power or output trannies. Just make sure you get them hooked up in the right places, or if you want, pay a qualified tech and better yet, watch the surgery in case you want to try another output tranny and DIY. Save the old tranny(s) just in case.
Mercury has a large selection of output trannies that would work for a single recto. Investigate the Axiom series. It's their top tier stuff. I have had wonderful experience with a Mercury Axiom Radiospares Enhanced model OT in my boutique Siegmund Blues Breaker. There is enough bottom end out of that tranny for chug, it's huge, as are the mids if so desired, and the top end is complex, incredibly rich in both even and odd order harmonics, the windings in that transformer are intricate, the original was in the very, very few first Marshall JTM45 bass amps and was both expensive to produce and purchase. Clean tone is to die for, has a very hifi quality to it with tons of detail. You hear each guitar's unique sounds. There are primary impedance tap choices on that tranny that when properly selected will match the necessary primary impedance for your amp's power tubes. It's a very spendy transformer but a Mesa amp deserves highest quality components placed within it. It will give back.
Nothing wrong with having a tone somebody will have a tough time chasing for a given amp type, and there are few better ways to do that than successfully swapping out an output transformer. Peace.