Another welcome from Calgary! The first time I went to the Stampede Drive-In on a hot summer night was in Signet convertible!! Cool car from your avatar picture but forum rules say we have a thing around here for more pictures :).
I seem to remember a vendor at the Red Deer Swap Meet selling old style tires but I've never looked very close so it may have been just the really old stuff.
On your starter relay I think you need to do some more troubleshooting, I've never had one go bad but that's me. Search the forum for "starter clicking" or "starter clicks" to get some ideas but essentially check all the connections and voltage in the starting circuit. If it clicks again try a good size screwdriver between the big and little posts on the relay and then on the starter to see if turns, it can be kind sparky if you hesitate, so don't hesitate. This heat wave certainly doesn't help but it sounds to me like the starter may be wearing out or sticky, I would also try tapping on the starter and solenoid with a hammer or tire iron, sometimes that will free it up enough to get it turn over but then you know it's in the starter. If you can pull it out a parts store can test it for you...
Good luck!
