"unacceptable under our standard to create a new power server project for each DB and redeploy"
If you are testing the PB part of the code, then you should setup a new project so you can test the new code. But i think you are wanting to just test out different databases?
if you are just testing some database changes, then why not just setup your login to 'repoint' to the database you want it to use. You use different db caches for this (the cache names can be created/setup at runtime via the webapis). Same exact concept as a SAAS deployment where each customer has their own database.
the big difference is that instead of deciding which icon to click, the user clicks which "database profile" to use after clicking the single icon. We name our testing databases "TEST" so that users know they are connecting to a test database, and then put up a messagebox that says 'you logged into test'.