I'm using Gnus, problem solved. Only 4 separate mailboxes, but it could scale to any number of sources, without trouble. The UI is the same as the rest of my environment, fits in perfectly, it's flexible beyond imagination, and tailored to my specific needs.

I used to use the gmail web UI before, but due to the problems you yourself outlined, I switched to something much more powerful, something much more flexible.

I love Gnus, now that I managed to set it up after more than 10 years of using Emacs, and resisting the temptation to finally give gnus a real try.