Probably Edmund can guess better than I can which setup codes those devices need and so he's probably correct in saying the 9910 lacks the setup code(s) you need.

The 9910 certainly has not enough memory to rely entirely on learning to support multiple typical devices (and other remotes do have that much). I'm not convinced the 9910 has too little to use learning for all of one device if you don't need any learning for other devices. It will vary by device but typically there is enough.

Anyway, if a 9910 without programming by JP1 cable isn't enough for the task then a 9910 (or other JP1 remote) programmed by JP1 cable is the best answer. Even adding the cost of the cable, the price is less than most (maybe all) those others and the end results will be better.