You said you made a page change for the channel (using "Renumber Controls" I guess?). Because there are "channel" bytes in most controls, but they are not being used for MIDI Channel selection, but for Element selection - just a different position in the sysex string.
Changing the channel is not possible in the layout, unless you change each and every control manually - quite tedious work to do. Please try and set your TG77 receive channel to either "1" or to "omni". Does that help?
And yes, the layout works bidirectional. All controls are set to "MIDI receive", means they will respond to changes being made in the TG77.