Really need the model number of the off the serial number tag; unless, you want to be secretive about it. As with it we can pull the wiring schematics. We need to know it a four poster is involved as if so you can have a voltage drop problem in either the positive side or ground return wiring.
First 10 ga is pretty small wire for a starter circuit; unless we referring to a walk behind mower. Most riders needs at least a 8 ga with a 6 ga being preferred.
I repaired a Craftsman 917.273811 back in the Spring that multiple bad connection (voltage drop) points in both the positive and ground return line. One was main positive battery terminal, one at the ignition switch, and one in the ground return line. So if you are jumping across the two large posts and the starter is working normally that eliminates the main battery positive cable and the main ground return. But doesn't eliminate anything in the trigger side of the solenoid circuit. Again you need to do voltage drop tests to find the culprit(s).
With a separate starter solenoid a help relay will probably not needed once the voltage drops are eliminated.