Ok - some photos of how I ran the wires out of the mirror into the door.
Starting point, with the cap and glass off:
Not shown, but un-do the plug on the inner door (door card pulled off) so that black wire harness has room to come out of the door. Don't have to feed the wire plug at the end into the door - I had enough length just leaving the wire connector at the opening where it goes into the door.
Pull mirror out and cut the little zip tie:
Spray some silicone spray or similar down the little channel (I used PTFE spray) and start working that black cable back and forth so you can pull it out from the door.
Take the two wires (yellow and brown at LH door) and tape them to the black wire bunch.
Grab the wire at the opposite end of the mirror and yank the bunch through. Might take some twisting of the wires and some back and forth as there really isn't much room, but it'll go through.
Note the somewhat atypical orientation of the BSM plug on the back of the mirror glass.
I popped off the black plastic frame of the mirror to run the wire out from the bottom, which looked like the "factory" pathway (and was same as where the mirror glass heater wires run). Three T10 screws hold it on.
Be sure to clip in the bottom of that frame as you're re-installing it.
Mirror heat wires re-connected and BSM wire run in provided holders on the bottom:
That's about it. Push the glass back onto the holder. Screw down the mirror back into the door.
Then try to figure out (and report back here, please) how you get those mirror wires you just ran into the connector on the door side of the hinge.