I just found a softlock:
So... you can put clothes into washing machine, while wearing underwear on exhib 3, than you go to shower, get naked and leave, than put on towel, wait until washing is done, than start again, now all clothes are in, now just go to dorm and strip yourself. And yea... now you are in dorm, naked without any clothes in storage and can't leave even for shower (requires exhib 4)... So yea... would be nice to have option to at least ask room mate to get new towel and maybe even depending on relation she could just refuse forcing you into leaving naked... or just keep the towel in room when undersing it.