Here's what I figured out, and was able to make it work. Which is awesome by the way, simplest solution I've seen yet.

This is a Chrome Extension, so you obviously need to use Chrome.

1. Download zip and unpack, doesn't matter where.
2. Edit the manifest.json file, under content_scripts section, change the value of js to background.js.
   "js": ["background.js"]
3. In Chrome, go to Extensions (3 dots in upper right corner, More Tools - Extensions)
4. Select Load Unpacked in the upper-left corner, and choose the directory you unpacked the zip
5. This will now show up as an Extension in Chrome.
6. Go to https://www.strava.com/heatmap. You probably have to login with your account.
7. Select the black S icon in your Extensions toolbar. The JOSM imagery URL is now copied to your clipboard.
8. Go to JOSM, Imagery Preferences, and update the URL for your Strava imagery layer. You'll need to manually add the tms[1,15]:, or edit the background.js file and add it to the url field.
9. You can update which heatmaps it shows and the color, by changing the 'both' and 'bluered' values in the url.