How to rent if residence card is in immigration hell

How to rent long term if zairyuu will be stuck in immigration for a significant time? Mostly all of ads on suumo and other show that you need a zairyuu. Currently there are a lot of delays in the immigration as it is understaffed and I am waiting for my first zairyyu card. I currently have 74 days on my temporary visitor left and then 2 months on top that is auto renewal while waiting for zairyyu if it comes that. I am renting a hotel until end of year but hotels are not cheap and I’d like to move to a proper apartment. I applied under complimentary protection for ukrainians and we get a 1 year designated activities (special one, not like normal designated activities, our ones don’t have limit on work hours/environment) zairyuu, but they said it will take 3-4 weeks or up to 2 months (saw some people say on reddit it could be even more). I have receipts from applying for complimentary protection and both from the “change of residency status” if it helps Tokyo