Did we sound like we'd been drinking?
You said "ideally, during a period of inactivity, the water should not drain back into the supply tank.
Which makes me think a faulty seal is the issue, rather than the filter."
I agree. I've also found few, if any, RV systems function as well as their household counterparts.
In my experience, so far. YMMV?
I would try cleaning the filter/screen to see of it improves the "prime time", but I understand that
logically it shouldn't. However, while you're fiddling with it, you could check/tighten the connections
to the pump. Might make a difference?
I have to clean mine now that I've drained for the winter. It only takes a few simple tools and a few
minutes to complete. It saved me a few bucks, as I was ready to replace mine, too.
Good luck with it, no matter what.