I wonder if the transmitter wouldn't screw with the ECH? Due to the extra draw, Ohms or whatever

I would think you have to come straight from the battery to power it, possibly put a little push button switch in the battery cover to activate it. There is a how to regarding a door button modified to a small button switch in the battery cover here already.
Pep Boys
NOS Push Button Switch; Momentary;
Part # 15610NOS SKU: 9969621