I believe the RF remotes will be fine controlling the dish joey boxes or directv genie clients. The problem you will run into is that (i am assuming the basement TVs are same brand and model) the TV remote will be controlling all the TVs at the same time due to IR.

The other areas besides the basement setup should work fine with the supplied satellite remote using IR and RF (i'm assuming these are just simple TV and Sat box setups with no AVR located locally in the room).

For the 6 TV basement setup. I would get 2 Global Cache IR boxes (~$90 each) and run IR to each TV (each GC iTach and do 3 IR connections). Then use an iPad and app like Roomie to control the TVs and the satellite boxes (Roomie can control both Direct and Dish with IP so no extra hardware needed).