If you need that many tabs you should take a look at tree tabs for firefox: https://addons.mozilla.org/en-US/firefox/addon/tab-tree/

it's the best thing to have all your tabs stacked on the side of the screen and still fit, alongside with a search bar!

Perhaps close them.

I'm assuming that was already though of.

Firefox does this.

Firefox originally had a preference for that, but they moved it to CSS, so you can modify it via an addon or with userchrome.css:

http://kb.mozillazine.org/Browser.tabs.tabMinWidth

nope. no tab overflow.