If you're handy with electronics...

Use the $50 to buy a spare remote for the DirecTV box. Pop it open and find the contacts for the "info" button. Solder wires to the contacts.

Build up a 555 timer circuit that will give you a momentary high output about once every several minutes. Interface this to a relay that will short the two wires you soldered to the contacts for the info button. ( In other words, the 555 circuit triggers the relay, that essentially does the same thing as pushing the button by closing the contacts.)

Now power the 555 circuit from a trigger output on your amp, and set the amp up so that the trigger output is energized only when you're in this mode of listening to music.

If you're not handy with electronics...

Punt!