I can think of one other thing to try:
For the functions that need a controllable repeat, try using the nec2 irp files with the usual device and function number. Maybe the URC will handle that differently. NEC2 doesn't send dittos; instead it repeats the entire IR signal.

I doubt you want to hear this, but a $20 RCA RCRP05B can send these signals, and just about any others. The repeats will work, IR signals with toggle bits will work, etc. Spend an additional $29 for a JP1 interface cable, and it will control any device which is controlled by IR.
Of course, there is no LCD screen.......