Well, I'm sure you've figured it out by now but you have to tell her about losing your anal virginity to a penis (or a strap on if you set the fetish flag that they are equivalent to true) first. Talking about your lack of underwear is exciting for Dr. Tra...er Synthea but the game wants the MC's first time to be somewhat special/she doesn't want to take that from you so you get the broadening your horizons comment until she knows someone else has been in there.
I think those are going to be for the replay feature in the bedroom which uses your current appearance, at least when the stacked image actually gets implemented. The only ways to open up the full bodyshop are the orgy and the office party. So I guess you've already found the fastest strat: miss a game, choose Luna for punishment.
Alternatively you might be able to meet Dr. Twig pretty early, but I think that that the flag that lets you work for him is the physical in stage 3 so it might be pointless. If you have forced medication on, OD on pink pills, and then stop taking your meds you can claim that the pills aren't working anymore and Antlers will send you down to R&D get checked out, or if you have forced chastity on and become a hermaphrodite with Dr. Synthea you can get hauled down to get fitted for a Demon Breaker 9001.
gregers is correct. Lose once, meet Kurt, talk about what happened at the tournament, learn what he knows about Bergmeister, do the tournament again. You tell Bob what to look out for off camera.