I finally got a satisfactory run under 14 minutes, though I still ended up missing the third elevator in the final segment. It should be possible to get below 13:30 with Edie, but research will be needed to see how close to 13:00 she can reach. Her speed isn't so much slower than Jad that her limit would be further from 13:00 than Jad currently is.

A lot of improvisation was done on the final segment of the game. I attempted to get the skip on the third elevator but missed it, so at first I tried to regain health on the blue door and missed that too. That turned out to be fortuitous, as missing the health allowed me to death warp to one floor above. From there, random enemy movement caused the remaining elevators to move into ideal positions, which allowed me to finish the speedrun as planned.

Achieved on MAME 0.266.