This may sound crazy but I've had this type of issue with Toyotas. The ignition timing gets severely retarded while cranking. Try checking the timing while cranking vs running to see if there's a difference.

If there is then what I did to confirm voltage drop as it's cause was to jump the starter with another battery altogether (jumper battery for starter totally it's own circuit-not connected to forklift at all) & then check timing while cranking- in my case the timing didn't change in this scenario. Not sure it's applicable but I thought I'd share