Boom 2 is 100% not compatible with a detachable TP. That is accurate information. The way you'd put an amp in the TP is the same as putting one in a bag. Anderson Power Pole disconnect and run 8ga wire through that. Your speaker wires would run through a smaller Deutsch connector, likely a 6pin for remote power and speaker wires leaving one pin unused

 

Was hoping under$800

 

You are on a SG so your best option here just like Chris said to begin with is the Amp in the fairing and run new speaker wires to the back. Ask Chris you shoot you a pic of what we installed on his bike, he has an ultra but with the the quick connects. All you will be doing is adding a Deutsch 4 pin connector under the back rest pad.
I don't know exactly what the guys will recommend for an $800 budget, but I am going to guess:
BT LL's
B54 amp
2 sets of Kappas
1 Deutsch connector
Power and ground wire
Inline fuse
Stinger 4000 RCA (or if budget doesn't allow, use cheaper but you get what you pay for)
and 25' of good speaker wire

Pete