i know nothing of insurance/loss issues unfortunately, but i had to comment on this:

(My second split-second thought while the other car was hitting mine was something along the lines of "Gee, I hope I don't have to go to the hospital; I have on old underwear!" I wish I were kidding about this... but ~~ sigh ~~ I'm not... )
After finishing the Monster Cookie Metric Century in April, I pulled on a skirt, ditched the bike shorts, and then realized I had forgotten to bring undies. Figured, oh well, what the heck, I am NOT sitting on that chamois for an instant longer, hopped in the car, and three blocks later, we were t-boned by someone running a red light. My third split-second thought (after "how's my pregnant friend in the back seat?" and "omg the bikes are on the rear rack!" was "oh s***, I don't have any underwear on!" So yes, I can relate

Hope you get the answers you need. If the damage truly is limited to the door, I agree with Zen and look for a junkyard door. But is there more damage that they're basing their "total loss" on? Frame/axle damage that's not visible?