When you pulled the sump off, was the pickup sealed up well to the oil pump?
How did the screen look on the pickup?
Maybe a dumb question, but you mentioned you had a new custom sump so are you sure you have enough oil in the motor that the pickup is below the oil level?
If you're concerned about piston/ring lubrication with all the cranking you're doing, shoot some WD40 down the spark plug holes until you get the oil pump sorted.
To avoid pumping fuel in from the injectors while you're cranking, you can pull the starter relay from the main relay box, and then put a jumper in its relay socket where its contacts would connect, whenever you want to spin the motor. I do this when I run a compression test. Without a key in the ignition, you can be sure the fuel pump, injectors, ignition, and all accessories are all deenergised, but you can still spin the motor this way.
Some people prefer to pull the main EFI relay(s) then spin the motor with the key, but my way is simpler, if you're careful. If you use a remote start button with a 2m lead and the right connections, then you don't need a helper to spin the motor.
Just make SURE you put the remote start button, or the jumper across the two points in the socket for the contacts of the start relay, not its coil, else you'll be in for a lot more problems than just the oil pump! If you accidentally short across the two wires for the relay's coil, you'll be sending +12 back to the ECU which could fry that output.
Here's a diagram of what I'm talking about - note, although this diagram is for an early LS400, the numbers on these points "may" not be the same for your start relay, so verify them first:
