The Remote wire won't overload any circuit you put it on. It's Just a signal wire to tell the board on the amp to turn on.
As stated before just run the wire to the column and off the ignition. It's one wire and it's easy to tuck away and hide.
As for the input for the amp, you said you are going to use the high level inputs in the amp.
sounds like you got everything in order.
Also what kind of amp and sub if you don't mind me asking. Good luck on the install and hope its goes smoothly!