Storing data as HSTS super-cookies is a topic that has come up several times in the past. This simple HTML file along with proper setup with nginx demonstrates that, thankfully, this is no longer an issue, since most major browsers now use separate HSTS sets for incognito modes. @ben174's hsts-cookie repo has a nice explanation of something similar.
However, it still is a super cookie, in the sense that deleting all history and wiping cache etc. will not clear it. Still, it is better than being tracked while in incognito.
A demo found here was working as of writing this! If you set some data, it should be accessible after you refresh the page, but will vanish if you open incognito/private mode.
The domains used are #.hsts.your-site.com, where # is the index of the binary bit. The client makes JSONP requests to nginx, which responds with 1 as a parameter to a function if https was used to call the request, and 0if not. The client can set the data by calling https://URL/set, which will return the HSTS header, forcing an https call next time. This data is then parsed.
At the time I write this, Wikipedia noted that HSTS can potentially have privacy issues, with HSTS being enabled being possibly used as a store of super-cookies. While I could find references that it had been fixed in most browsers that incognito modes used a different HSTS set, I just had to be sure!
I've tested that the hack doesn't work on Edge 16, Firefox 58, Chrome 64.0.3282.186 and the Safari on my iPad, whose version I'm unsure about.