Sling certainly won't do anything, They have a list of dozens of boxes they don't even support and that is much more important. It's an interesting exercise though and I might be able to help. As I understand it you want the 311 Binary code timings matched to the TR-40 'image' ?
I cannot tweak the built-in codes so the first thing to try is a Custom Dish Remote to see if it has any the right binary code timings, give this one a try.
Later; Sorry, just realised it's a waste of time. Sling have removed the functionality to match remote images with Custom codes in the 500 so I cannot improve on your present situation.
Thanks for the information. I wasn't sure if there was a way to tweak it or not. I looked into custom remotes years ago for my original red Slingbox PRO. I wanted to support a Magnavox TB100MW9 and wound up finding a lot of information on custom remotes. However, when I discovered I could control my TR-40 using a DISH configuration, so I gave up on the Magnavox and went with the TR-40. I was quite excited to see the TR-40 support in the Slingbox 500 but that excitement went away when I saw the timing problems. So it was back to the DISH 311 configuration.