Oil Pressure

Start the car, oil pressure gauge reads 40+ at idle. As the temp comes up,
the oil pressure goes down-to zero (still at idle). Step on the gas, pressure
goes up.
There are no secondary indications that the Oil Pressure is zero. The engine
does not sound different, the coolant temp does not change, the engine does
not run differently.
What I did:
  Change the pressure transmitter (no change).
  Change the pressure transmitter screen (no change).
  Change the oil and filter (no change).
  Put a shop vac on the transmitter port to pull out any junk (don't knock it till
you try it-but no change).
Looking for ANYTHING else to avoid getting rid of the car. It's 14 years old
but great except for this issue, and the fix is going to cost 25-50% of the
vehicle value.