Any Paperwhite should do, they all run common firmware I think.
I wonder if it is just an older Javascript and a few commands need to be adjusted. I had an app that Googlebot couldn't render that I worked on this week, and a couple of "use strict" statements and it was working fine. (Googlebot uses Chrome 41.)
A google search reveals this:
"Newer e-ink
Kindle devices, like the PaperWhite, Oasis and Voyage running firmware 5.x support the ES5 version of JavaScript and some HTML5 layout features, similar to an original iPad running iOS 5.0. You can inspect the source code for the browser, which Amazon supplies in their open source compliance download package. It is based on the WebKit sources circa 2009 with some customizations for e-ink rendering. The browser passes the Acid 3 standards compliance test with 100 out of 100 tests passing and almost totally matching the reference rendering."
This may also help:
http://html5test.com/compare/browser/kindle.html
The iKommunicate app has its quirks but it works, and Sailgauge works with some modifications. Really if we could mash up the two of those we might have a decent 80% solution. Of course the configurability of Kip makes it so awesome.
Sadly, the cross section of people in the world with a signal k server and who wish to use the
Kindle as a display seems to be about 6 people! I'm not sure why others don't think it is so brilliant. It's cheap, you can read it in full sunlight, and best of all kid wants nothing to do with it.