That would be one option, but I don't know if we would get another loan if the big one is already registered with Schufa.
I would actually just straightforwardly ask the kitchen studios. That's a very common topic. When does everyone install a new (and maybe the first NOT from Ikea) kitchen? Exactly, when they build or buy a house. You are certainly not the only ones considering financing that as well.
I also don't know how severe the "big" loan is in the Schufa. Schufa entries are not negative per se. As long as a loan is always properly serviced, it can also be a positive statement about your creditworthiness.
I can hardly imagine the house loan in the Schufa being an exclusion criterion for further loans. Otherwise, homeowners wouldn't be able to finance cars anymore, while tenants could.