"what device could I put across the dummy load that would show if even a very brief period of RF went to the relay's RX port?"
The "old solution" was, as was used in the Drake B lines, a small light bulb in the RX antenna line (I forget the number, a # 47 has the same filament). If over-voltage is applied, it will light up, go to high resistance and possibly blow open and effectively disconnect the RX antenna source.
A modern diode could be used from RX line to ground (or a pair). Diode(s) will add a small amount of capacitance to the RX antenna line, but that shouldnt be a problem.
Its critical especially in TR relays to have clean and properly timed contacts.
"Also, how can I measure the voltage the relay is having to switch given it's in the house before the matching and loading coils outdoors"
Calculate it from impedance and power level. V = (8PR) ^ 1/2 (P= power R = resistance of the feed at the relay contacts)
ALso realize that a transient fault in the antenna can send a large voltage spike back down the line.