The Emperor charged H a huge amount for the Emperor's participation. Part of that was just transporting the troops. Remember the fight scene where the couple visits the H's planet and watches the Baron's nephew fight? The couple notices how everything on the planet is in financial ruin. The Emperor didn't lose money in the short run by switching management, and he had the prospects of "encouraging" H to do better in the future because the Emperor had demonstrated that he could get rid of any house he wanted to. (Granted, H also had the ability to tell the other houses that the Emperor had helped him get rid of A, but that wouldn't make the other houses love H. If H told what the Emperor had done, both H and the Emperor would look really bad.)

And, IIRC, the Baron's promise to the Emperor is to bring lots more money into the Emperor's pockets after he gets Dune back. When the Baron sets up the one heir on Dune to be hated (by being way too harsh) and that heir, instead of being ruthless and bringing in lots of money, experiences everything falling apart (due to Paul's and his mother's training and consolidation of the Fremen, and using them to strike at the heart of spice production), the Emperor decides to come to Dune himself and fix the big mess H has created.

I could be wrong. This is just what I got from it.