No start with new wiring and battery relocation
First I do not understand what you mean by "newer starter relay." Can you post a shot? Is it 3, 4, or 5 terminal?
1...The one in the photo is a 69/ earlier STICK shift which grounds the coil through the relay mounting bracket.
2...ANY automatic, and not "newer" had 4 terminals, and the stick cars 70 and later used that 4 terminal relay. Only difference is the added terminal is for the relay coil ground---which is grounded by the automatic neutral start switch, or by the clutch switch in a stick car
4...The "later" 5 terminal, used on Jeeps and I think Dodge pickups, had a terminal that came alive when engaged and sent power off I guess to the ballast during cranking. This relay, even tho appearing different, works just like the automatic relay except the solenoid terminal was replaced by different terminals, and then the added terminal at far bottom left

So, if you have a 3 terminal, make sure the relay bracket is grounded, and there is not much current there. The mounting bolt to the body should be fine.
Make sure you have the starter signal from the key to the "push on" terminal which is the coil of the relay.
IF you have the 4 terminal, the remaining push on terminal must become grounded. Again, this either goes to the NSS on the automatic, a clutch switch if used, or to ground. This terminal functions in place of the relay mount on the stick relay
I doubt you have the 5 pin Jeep one, but the picture should relate the hook up. Same as the 4 pin, ignore the added 5th pin.