Yeah, that is correct.
I swapped in another relay and it cranks just as fast by the key as it does by crossing the terminals on the relay.
New ones are around $30 from the auto parts stores, which sparked the memory of a member here mentioning the process of disassembling them to clean the contacts.
I have maybe 15-18 of these in the shed in all stages of condition. I could try taking them apart and cleaning them up.