Try a few basic things,
Actually measure the voltage at the starter using the battery first and then the GPU with a meter. The cockpit instruments are not good enough and can tell you lies.
There are different paths that the current takes between the two start regimes.
Another problem you may have - The "generator" part of the starter/generator is always generating it is just isolated during the start. If it is not isolated as the speed increases the generator starts to cancel out the starter.
I would guess that on a GPU start the start portion is isolated completely with a different method as you notmally cannot charge the GPU.
I would be looking in the EMB for bad contacts, corrosion, loose or broken connectors etc.
It ain't rocket science but you should do something before you burn it.
On another point make sure that your DC system is in good shape and operating correctly with correct parts.
Several demons have popped up in this area on the Arriel causing accessory drive failures and subsequent engine failures.