Starter clicks using the key, engine starts by jumpering the relay

When you use the screwdriver you are bypassing the relay.

If the relay contacts are bad then maybe you are getting just enough current flow to have the starter solenoid move

You will need to look at your wiring diagram to be sure.

Righty Tighty said

I connected my meter to the solenoid post on the relay and got 0 volts with the key in the start position

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0 volts on that wire says the relay is not engaging OR the 12v to the relay to make it engage is not functioning OR the contacts in the relay are bad.