I've modified two Thiele mikes and made them both into useful studio gear. The first I worked on was my own, an M1 (cardioid only) I bought on Ebay. All I did was remove the power transformer and rectifier, and install an output transformer in the newly available space. Then I built a new external power supply. It now sounds about as cool as it looks. Ridiculously trashy as an instrument mike, but hyped and rock on lead vocals, which is all I use mine for.
More recently I modified an M4 (cardioid and omni) for a client. I removed the power supply, built a new external supply, installed an output transformer, and this time I rearranged the internal components to put the vacuum tube down below the top deck so it wasn't in the way of the capsule. It's not like you're going to get a clean omni pattern out of this thing anyway, but it can't hurt to get the tube out of the way. The omni pattern is at least useful on vocals when you don't want proximity effect or when you want more room tone.
I've got a basic schematic of the M1 on my web site at http://www.rollmusic.com/projects/thielemod.jpg and you can imagine how the M4 differs (it adds another diaphragm, another capacitor, and a switch).
My more recent work used a more sophisticated power supply, including regulated heater supply. I used a Triode transformer in my mike, and a UTC Ouncer in the other guy's. I think ideally you want about a 4:1 step-down transformer. Note the need for a coupling capacitor between the cathode and the transformer.
This microphone has two high-gain triode stages, originally 12AX7. This gives it a *very* hot output and very low headroom. I found using a different tube helps a lot. I think I'm using a 12AY7 in mine right now but I should really switch to a 12AT7 or 12AU7. This lowes output level and output impedance. Even with a step-down output transformer installed, this is a good idea. Otherwise, the tube circuit seems to clip prematurely.
But don't bother modifying your Thiele until you've first confirmed that the capsule works. There's not much point in doing all this work if the M7 is shot. Reskinning it is probably not an option, since it's PVC.