Finally got around to trying out various solutions. First, I tried wiring it as suggested by the schematic posted by Steve Anderson (thanks again!). Unfortunately it made no sound at all in that configuration, so apparently the pinout is different on that headset, oddly enough.
I then tried the approach outlined in the DPA adaptor schematic from Jens (thanks for that), and this works quite well! I ended up connecting both the white and red wire from the mic to the "hot" wire and the shield to pin 1 as suggested, and now the mic handles higher SPL and clips much more gracefully - the harsh distortion they had before when overloading is gone. Also the signal is much hotter, so now I have to engage the PAD on the transmitter, but then it's fine. I'm not sure if the mics are handling exactly the same SPL as they do on a MiPro beltpack, but it's at least close if not identical.
Incidentally, I measured the Shure bodypacks providing 5.2V of bias and the MiPros give 5.9V, so that's pretty close.
Thanks to all who chimed in! The problem is pretty much solved now.