infinite/sustainable hosting of a web-interface to a research database
I have the impression that quite a few university libraries are very interested in preserving and making available other things than just books. So talking to your university librarian would be my first stop. Even if your university library does not have expertice in this field, they may know of such a project somewhere else that you can apply for.

As to someone else maintaining the web-interface for you, I would not count on that happening. That will cost someone time and money, and unless you are rich enough (and willing) to set up a fund to preserve your project, you cannot count on someone else doing it for you. Instead I would keep the interface as minimal as possible. It may not look pretty, but it is more likely to keep working.