Start with voltage measurement.
Charged 12V lead acid batteries should have at least 12.56V at rest (no load, ignition and all lights, etc..., off). Below 11V at rest and you likely have a dead cell.
Did you say you put two Group 31's in with 625CCA each? In parallel this should give you roughly 1250CCA assuming a full charge. If you only have one battery with 625CCA, it's probably too little current. Low voltage and low current melts starters -low voltage means lower start speed, higher torque load since you never get up to a high enough speed to overcome much of the internal friction - this leads to higher current draw, and current will eat up a motor at these levels. I do believe even civilian models that had a 6.2L will have two parallel batteries.
Other thing to check is the condition of the brushes in the starter - I'm presuming you have an original 27MT - the lower-speed direct drive starters draw a bunch of current and that is really hard on brushes. Worn-out brushes or brush springs mean less sustained current gets to the motor.
As others have said, I recommend a big fat ground to the engine. The starter motor will draw much more power than the alternators will ever generate (27MT can draw more than 5kW during a start), so a big fat ground cable (>1GA) from the block right back the battery(s) will get more voltage and current to the starter motor. A few (>2Ga) ground straps to each head where the alternator brackets attach will reduce the current that goes through the head gasket and head bolts for the alternator and the glow plugs. Steel has about 1/5 the conductivity of copper, so the less of that you go through the better things will perform. Remember that manufacturing cost was a big concern for GM, so they cut as many corners electrically as they could reasonably do - there are some improvements that can be made on their design without the same budget limitations (eliminating ground returns was a common theme with cost reductions in the 1980's GM vehicles).
I know that you're not asking about moving back to a 24V starter, but one thing to consider is that for
the same power (watts), you need half the current at double the volts. 5kW / 12Volts = 416Amps AND 5kW / 24V = 208A. If you were to use a 24V 28MT gear reduction starter, the internal motor will spin much faster (as gear reduction motors do) and would not be as easily affected by less current availability as the gear reduction handles the torque multiplication (volts and winding type affect rpms more in a DC motor).
For my money, a pair of 1100CCA Group 31's in 24V configuration with a 24V 28MT is the best you can do for a 6.2L diesel. My
