Low oil pressure

I've got a 2011 silverado 1500 with a 5.3 engine. I
recently had an issue with my oil pressure
dropping to 0 shortly after start up. Needle would
slowly drop until the "stop engine" warning came
on. Took it to the dealership expecting a sending
unit problem. Sure enough, they changed the oil
and filter, current Guage would read around 10 and
drop, mechanical guage read 35. Both at a warm
idle. I put an AC Delco sending unit and new screen
on. Ran it about 45 minutes at a steady speed.
Pressure started at 40, when it warmed up the
pressure dropped to 20 then to 10 till the warning
came on again. Could this really be yet another bad
sending unit or is this something worse? BTW,
when the " shut engine off" warning comes on I pull
over and immediately check the oil. It always
shows good on the dip stick. After a minute or 2
the truck shows about 20 psi again and is good for
a while. Really need help with this...