You can very likely do this yourself and save yourself the $99. Nevertheless, it's nontrivial because installers make use of 2 devices that may
look like splitters but which are not. Connecting them all up correctly is a little confusing, but it can be done.
The thing that
looks like a splitter on the back of each receiver connected to the two satellite tuner inputs via 4" cables is called a "DishPro Plus separator." Leave those where they are (on the back of each receiver) when you are moving things around. That part is easy.
Now for the confusing part. The other things that look like splitters, but which are not splitters at all, are called "diplexers". They always come in pairs. These allow you to run RF TV signals over the same cable as your satellite antenna signal. They were originally designed to combine the satellite antenna feed with a conventional OTA antenna. But with Dish Network "Duo" receivers, they are often used instead to backfeed the TV2 output to other TVs. This is probably what your installer did to feed your bedroom and basement SDTVs.
So, in order to move your study 222 into your bedroom, you are going to have to locate at least 3 of your diplexers, figure out what they are doing, and recable everything to do what you want. It's a bit of a puzzle, but I'd say if you're tech savvy then you'll regard it as a challenge and get it done in no time.