If the box to be controlled is something other than address 1, then the setup code is irrelevant and all commands will have to be learned, unless you have a JP1 cable, in which case, you simply select the proper address in the JP1 software and download it into the remote. If you are using address 1, in AUX mode, you must specify the device type. So you must use SAT 0775 (most likely), not any other device type (TV, AUD, etc.).
Will any of your Dish remotes operate the new box? If so, clear a few old learns to make room for enough new ones to test. If any are successful, then clear all of them and learn all the commands from the working Dish remote. Just remember, you only have enough learning memory for a total of 20-30 keys across all devices.
The key really is determining or setting the address for your box as posted early in this thread. That will determine what code to use and whether you need to do any learns.
IMO, your 15-2116 is every bit as good as any harmony if you start using the software. It's much more powerful and sophisticated than harmony software since it can do unlimited macros, nested macros, recursion, unlimited devices, fast macros, conditional branching, just to name a few things. And has a fully graphical programming interface, unlike harmony. I used 15-2116's for many years and still have a few in my closet. I never had any issues using them with any of Dish's 32 possible addresses. I just pick the address in the software as I said. With the JP1 software you never have to use learns except for signal analysis.