One way to do it is remove the capsule, (which by the way, doesn't "couple" to the body acoustically), unsolder the 2 wires and then remove the xlr connector. Throw the body into a pot of boiling water. After a few minutes, the hot glue will soften and then you can pull the transformer out. Now, take a look at that transformer. Ever seen such a pos? Be glad you tossed it away.
Now, wire up the 2 pins on the capsule to the xlr connector. I don't remember polarity, so you can check it against a stock 57 by putting the two mics together and matching gain. Pan to center and if they add, a-ok. If they cancel, reverse the wires for correct polarity.
Notice the large low end, somewhat like an SM-7. Notice the clearer top end, that's cause you removed that crap transformer.
Older Unydyne III's should be kept stock as they are rare and sound so much better than the Mexican 57's.
I noticed the sonic changes on these back in 1990. I called a shure engineer I knew for an explanation. He told me no changes were instituted, but original stampers and dies were sent down to Juarez. If you know about record pressing, stampers wear out and need to be changed regularly. As far as I know, old stampers and dies are still being used. This was the main source for the sonic changes in the mics.