I have a suggestion: You could optimize the website to be easily readable and navigable on the Kindle's web browser, and recommend it as an option. I've often found it to be the easiest way to get non-store books on my Kindle. I've also noticed that cover images are handled correctly when the ebook is downloaded straight onto the device, with no need for a separate image file.
A hurdle for this though, is that building a good website for the Kindle browser is a pain, as the browser's support for various html/css/js features and standards is all over the place, with no debugging tools available.
A hurdle for this though, is that building a good website for the Kindle browser is a pain, as the browser's support for various html/css/js features and standards is all over the place, with no debugging tools available.