I have a way to send links to Instapaper FROM my Kindle, based on a tip I read here: http://www.mobileread.com/forums/showthread.php?p=1315115#post1315115.
1) When you're on a page you want to add to Instapaper, using the "Enter URL" option on your Kindle, cursor to the beginning of the address, and type in "tinyurl.com/create.php?url=" (it's short enough to memorize so you can do it quickly). You now have the address you added AND the page address in the URL box together. Press "Enter" to take you to the tinyurl.com URL-shortening page.
2) Assign each page a name following some system you make up using VERY SHORT names that you can REMEMBER (such as "jan0120111" for the first file you want to send on Jan 1, 2011). You might want to put a random letter in there somewhere to make it more likely no one else will be using your filenames!
3) Go to your email account on your Kindle, in which you've already set up a contact for the long, weird email address of your Instapaper account.
4) Send an email to that address, in the body of which you've typed the shortened name you've just assigned to the page you wanted to send.
The page will be added to your Instapaper account. It's hardly a streamlined, one-click solution, but it does work and doesn't take too long.
Instapaper's "Browse" feature is provided by givemesomethingtoread.com and the RSS feed for what it presents in the app and site is available at http://givemesomethingtoread.com/rss/links
I suspect the collection is not autogenerated from the RSS feeds provided by these publications, but its manually managed by adding articled where there is a link to the full version.
Best Answer
Warning: This works, but not perfectly as formatting can get a little screwy.
FWIW, I also tried downloading the raw HTML and pasting it into Glitch, but the PDF character count is like 20k, and the Glitch server timed out. Also, I'm not sure that Instapaper works on Glitch.me websites.
If you know of a better solution, please lemme know.