I... kind of have a solution, but it's at a compromise. Read the whole answer first.
(Note that if you manually installed Firefox developer edition to /usr/lib/firefox like I did, you need to back it up as it will be replaced. Also back up your ~/.mozilla folder in case the following fails and wipes your .mozilla folder.)
So first, add the Firefox beta ppa with sudo add-apt-repository ppa:mozillateam/firefox-next
Install Firefox beta with sudo apt-get update && sudo apt-get install --only-upgrade firefox
Now run firefox -P
and your developer edition profile should still be there. Select it and open Firefox. You'll have the latest beta on the ppa, as you can see with "about Firefox," and you'll also have your developer tools and global menubar.
HOWEVER, I'm pretty sure none of the tools specific to developer edition will update. Only the base browser will.
Correction: there aren't tools specific to developer edition that beta doesn't already have. By upgrading to beta, you aren't losing anything; it's just more troublesome than keeping developer edition.
I immediately went back to my manual install with no global menu (and also a super annoying bug where the url bar doesn't autofocus on new tab) when I figured this out, so you may not want to follow these steps. But if you really want the global menu fixed now and also are fine with the current state of all the developer tools, this may be worth it. See above.
Otherwise, I guess you'll be waiting with me for Mozilla to patch this bug. Bug resolved as wontfix since it's a lot of trouble and Unity is dying anyway.
Sucks that the only answer to this is to scrap developer edition and install the beta ppa (which has the Unity integration, of course) but that's all I've got.