FF: page find focus issues

There are a number of issues with Firefox and the find functionality:

• Often when entering a string to find in Firefox the focus will briefly leave the find prompt then return with a random new selection or cursor position. Sometimes it returns to the start and this results in words entered backwards (typing "next" results in a search for "txen"), other times the whole entry is selected and then replaced when you press the next key ("nex" -> "t").
• Sometimes the / key binding brings up Firefox's quick find prompt instead. Sometimes pressing / brings up the prompt but does not focus it at all. Pressing / again brings up quick find underneath it.
• Ctrl+Backspace inside the find prompt does not erase any characters/words, unlike most text input fields (may not be a firefox-specific issue?)

I've found a possible reference to this so it may be a known problem but I couldn't find a relevant open issue tracking it.

Start with the Firefox find-functionality behavior described in the issue and review the referenced Vimium pull request #2476. Reproduce the focus, slash-key, and Ctrl+Backspace cases in Firefox, then trace the find prompt entry point. Done means the prompt retains focus and selection correctly, slash opens it reliably, and Ctrl+Backspace behaves as expected.