I just went through something like this with a Nady TCM-1100 I picked up for $119 on eBay. They said it came with a 6072A tube (a special 12AT7). Well, those at Nady are both idiots AND liars. For one thing, it was a 12AX7 tube! It said so right on the glass. Next off, a 6072A is a 12AY7, not a 12AT7.
With a 12AX7, the mic sounded bright and scooped. Lows and Highs were pronounced.
Added a 9 pin socket so I could change tubes easily and tried a 12AT7. It sounded a bit fuller, but all the 12AT7's I used created that "wind" noise after they warmed up. Nixed that!!!
Tried a 6072A (12AY7) and the sound really got full, round and smooth.
The areas that make the biggest changes in sound are the capsule, the tube, and the transformer. The capsules are made by 797, which are fine capsules, so no real need to upgrade those. If the tube you have IS a 6072A, try different NOS versions to get the timre you like.
Try different types.
The 12AX7 has a gain factor of 100
The 5751 has a gain factor of 70
The 12AT7 has a gain factor of 60
The 12AY7 has a gain factor of 45
The 12AV7 has a gain factor of 41
The 12AU7 has a gain factor of 19
The higher gains push the low and high end frequencies and saturate the transformer. A good transformer can handle this, but a poor trafo can sound bittle and muddy. The mid ground gain facters won't saturate the transformer as much, so the overall is smoother. The lower values smooth also, but increase floor noise as the preamp level is raised.
You could also replace the transformer ,with a special tranny that is produced by Cinemag. Great trafos.