I'll be camping next week, so I'm adding my notes on how to get Edge compatible from here.

First you're going to need a VM of Microsoft Windows 10 with a Developer's Edition of the Edge browser (download the one labeled Microsoft Edge on Win 10 Preview).
https://developer.microsoft.com/en-us/microsoft-edge/tools/vms/

When you download this, it will be in a .zip, and on a mac, it will unzip into a .zip.cpgz file, which will unzip into a .zip again. This is an endless loop, and the solution (on a mac) is to brew install p7zip and then 7za x file.zip, as documented here:
http://superuser.com/questions/626721/trying-to-unzip-file

You can then load it in your virtualization software of choice, I had no problem with the VirtualBox version.

After you have the VM running, you should shut it down, open its settings, and share a folder between your system and the VM, perhaps just the whole metamask-plugin folder, so you have access to both the dist and builds folders from the VM. I recommend setting it to auto-mount.

You'll need to turn on developer extension mode on Microsoft edge, by visiting about:flags in the Edge URL bar, and checking the Enable extension developer features box.

Once resetting the browser, you will be able to (try to) add an extension by:

1. Click the ... button in the top right of the Edge window to open the main menu
2. SelectExtensions.
3. Click Load Extension.
4. Navigate to a built extension folder.

The first error I've gotten was about needing to set a persistent value in the background.js file. Sounds like there are some API differences between Edge and Firefox after all!

The Edge extension APIs are documented here:
https://developer.microsoft.com/en-us/microsoft-edge/platform/documentation/extensions/api-support/supported-APIs/