Brush and commutator could be dirty/full of crap and shorting/not flowing full current to the proper windings in sequence. When that happens you loose torque. Same issue can occur with the solenoid contacts, or the conductor pathways to the starter Are limiting current. You checked voltage at the batteries while cranking. You can check those same cranking voltages at the input and output of the solenoid and the input to the motor. In a perfect world they should fall off about the same as the battery, or only slightly more due to line losses when cranking. If they drop off significantly farther, this indicates a weak connection/contact unable to feed enough current to maintain the voltage under load.
its a 3126/A1 so you don't have a instrument shunt in the ground path and should have a single large gauge ground wire from batteries to front of motor housing. Current has to flow around the whole pathway, so don't neglect that half of the circuit.
I recently troubleshot something similar on my 30HP diesel tractor. I incorrectly assumed my 05 vintage battery was finally giving up the ghost, but when I dropped in another battery it did the same thing. When I finally dug out my meter and my brain, and measured voltages, I had nearly the same voltage drop all the way to the starter motor input. Pulled the starter, cracked the case and found the brushes and commutator full of greasy brush dust. Cleaned it all up, re-assembled and installed it and it spun the engine great. Put the 18 year old battery back in place and been running it all winter with it, still cranking strong…
