I bought one of those as well, for the same reason. I posted some notes from my analysis of it here: <http://recordinghacks.com/microphones/monoprice/600850
In a nutshell, it's a three-pattern FET condenser. The audio circuit has an output transformer. The DC circuit (on the second PCB) is a standard Chinese implementation of the oscillator found in the Schoeps CMC5, with a second voltage doubler on the output -- needed to hit the +120V required for Fig-8. Typical of cheap Chinese stuff, the whole thing was built with forgettable parts.
A signal injection test revealed no in-circuit EQ, which suggests that the stock 32mm K67ish capsule is not a great choice (unless you like bright microphones). A K47, M7, or CK-12 style capsule is likely to work better with this circuit. Whether you can sandwich a 34mm capsule into the 32mm rubber harness is another question. I guess you could fabricate a mount for a 34mm capsule; that wouldn't be terribly hard if you have some CAD experience and a 3D printer.
You could measure the transformer's turns ratio using the procedure here: <http://recordinghacks.com/2017/08/29/how-to-measure-transformer-ratio/
You could also inject a swept sine wave to check for frequency response and distortion characteristics. If it is a low-ratio transformer, it's probably fairly clean. If it is a higher ratio than about 5:1, chances are it's going to exhibit some funky artifacts, especially at low frequencies.
Whether it's worth replacing the transformer depends a lot on what else you plan to do with the mic. I don't personally think that capsule will ever sound good. The circuit could be upgraded with nicer parts, but unless you have a schematic (or want to trace the circuit to make your own) you won't really know what you're changing. The challenge with a lot of cheap mics is not just that they're built with cheap parts, but that they commit topology crimes too. Those problems can be difficult to find or fix without a schematic.
Had this mic not disappeared from the Monoprice catalog so quickly, I would have cooked up a retrofit mod kit for it. It's a solid piece of metalwork. You could keep the DC board and switch board, and just replace the audio PCB and transformer. I'd pursue that rather than get hung up on esoteric capacitor upgrades of the sort held in such high esteem on lesser forums. ;-)