Sorry again Fletcher, we don't make power supplies for mics. There are quite a few folks who do, though, and the requirements aren't that critical. The schematic JJ Blair posted in this thread looks right to me. If your power supply maker doesn't understand what's going on with the voltage dividers in the B+ and heater circuits (ask them to explain it), find someone who does.
or at least he has spoken about them with authority more than anyone else I've ever spoken with about those mics
...that's just because I've dissected enough of them (mostly broken ones!) in the process of understanding them well enough to replicate the acoustic design of the capsule. Originally this was for the Groove Tubes MD-3 mics and with some more refinements our C715. We didn't use anything from the power supply though.
The power supply of a C37A makes about 160 volts B+ if I remember correctly. As shown in the diagram, the heater is fed 6 volts DC, floating at about half the B+ or 80 volts above ground. This approximately sets the capsule polarize voltage which is tapped off the cathode. The C37p does it entirely differently with a separate dc-dc converter.
The audio output stage is just a coupling cap (switchable to determine the low frequency rolloff) and a transformer, which I think is around 4:1. This produces a low output level (since it's already coming from a nominally unity-gain cathode follower amp) but that just means you need a little more gain in the preamp. Cathode followers don't like to see much load, so an impedance step-down is needed, and with that goes a drop in voltage.