I use Tree Style Tab for this, although I hate the actual tree functionality - it just happens to be the only reasonable vertical tab solution I've found. Unfortunately, it seems to get a little bit laggy with more than a couple hundred tabs.
Unless you specifically tweak the UI to enable really small tabs, which is among the first things I do on a fresh install. Favicon + a small number of pixels for padding, way way less than Google allows me to get away with! Slap on a bunch of tab groups and I'm set.
I'm quite comfortable with a tab group filled to the point where the tab bar only displays favicons, but hasn't gotten to the point where it lets me scroll yet. That way I can rely on spatial memory to get to the right tab, without necessarily seeing the title!
Of course, searching for the right tab is an option, just like you said. I love the fact that Firefox also activates the correct tab group automatically.
Also in Firefox the tabs never shrink to just favicon, the tab heads become a scrollable list. Much better than Chrome imo.