I have a Harmony 880. I had to do this with 2 Sony AV receivers in the same room.
#1 get your DISH remotes set up with separate IR addresses. I forget what Dish calls this but your 722 remote should be on a different IR "channel" than your 622 remote. Your Dish remotes MUST WORK CORRECTLY FIRST. This is very important.
#2 set up your 722 in the Harmony software.... I just used the web client. Update remote. You should now have your 622 activity and your 722 activity. You're not done yet.
#3 I can't remember exactly where in the Harmony setup this is... device I believe, but what you're looking for is "Confirm IR Language". It will ask you to press a few buttons on the remote and it will figure out the IR address to use for each one. So make sure when it's asking about the 622, that you have the remote for the 622 lined up with the Harmony. And when it's asking for the 722 remote, same thing. If you inadvertently switch remotes you'll screw this up.

All that means though, is that you'll have to repeat #3 again..... not start all over.