So far, there doesn't seem to be anyone with the truck configuration you're looking for who's willing to post. However, I do know that the 8.1L engine was not available on the 2009 GMC (and probably Chevy too) 2500HD. The 6.0L was the standard engine and the Duramax/Allison with a 3.73 was optional. I'm no expert on the history of GM 3/4 ton trucks so you'll have to do your own research on finding out if the 8.1L was ever even offered in a 3/4 ton and what year it was dropped.
As I mentioned above, I have the 6.6L Duramax/Allison with a 3.73. Below is what it tows.