The following works for gnome3 terminals. It uses xdotool to automate interaction with the gnome terminal menu, since the available keyboard shortcuts are currently limited.
I have created two profiles. The top one in the Terminal->Profiles menu is my default, and indicates a local machine. The second one is my color scheme for a remote connection to machine66.
I then defined the following aliases in my bashrc:
alias first_profile="xdotool key F10 Right Right Right Right Down Right Return"
alias second_profile="xdotool key F10 Right Right Right Right Down Right Down Return"
alias go66="second_profile; ssh remotemachine66; first_profile"
The first_profile and second_profile just use xdotools to click f10 (open the menu), and then traverse right to terminal, down 1 to profiles selection, and then select the first or second profile.
go66 first calls second_profile to set the colors, ssh's into the remote machine. On exiting ssh first_profile is called, returning the profile to the local profile.
It's clunky, but it works. I'm happy to hear refinement suggestions.