I ended up using Mogami W2893 for all of the internal wiring. Both because the 4 cores are different colors (which was a huge bonus) and because it was far more flexible than the (also) 26AWG Canare L-4E5C.
Maybe, just maybe I'll be able to attach the (huge) pics here (click for larger versions):
Starting with the left driver, I removed the earpad.
I then removed the ring and foam covering the driver.
Took the driver out of the cup, cutting the wires in the process (this was one of the hardest parts, mentally anyway), I then desoldered the wires you see here, which lead to another part of this post.
Enlarged the hole in the cup for the mini-xlr (I had to do this again to move it down a fraction of an inch later on)
(not pictured): Inserted the mini-xlr, which I had previously wired and "welded" it in place using Gorilla epoxy
I then wired up the driver (configuration I have is different from stock due to the ground tab breaking off on my first attempt, thank you TrollDragon for helping me through that to make sure the driver could still work)
Put the driver back in its housing (almost forgot the dampening ring too!)
I also twisted up the 2 paracord-sleeved wires that go to the right driver. Not pictured, I put a tiny bit of adhesive-backed heatshrink over the wires in about the center to help keep the wires twisted.
I put the left cup back on the headband (2 small screws is all that holds it on) and continued to the right driver. I took it apart as above and removed the stock wiring. I then (slightly) widened the hole the wires come into so that both sleeved wires would fit (did this on the left side too). Soldered the wires in place, put the cup back together and reattached it to the headband.
A shot with the cable I made for them. Will be making a few more, I'm sure.