Here are your parts
Replacement parts for GE GSD4020Z00BB | AppliancePartsPros.com

Is there a way to extend the time of the pumped drain cycle?
No

Is there way to bypass the wash cycle and switch to the pumped drain cycle to remove the water?
As far as I know you just move the timer to a position where it should pump out and close the door.

First remove the kick plate and check if the wash/drain solenoid is being pulled all the way down.

Next remove the drain hose from the sink drain or disposer. Sometimes crud can build up where the hose goes over the fitting.

Next check the Piston & Nut Item 564 in the "Body parts" section. It is under the filter screen assy at the back of the tub. Unscrew it. Left hand thread, I think, am not sure about this.

Could also be stuff in the pump or sump but usually you would notice poor dish wash results.

Could be some other things but the above should keep you busy for a while.