With the 3.1 there is no real oil pressure indication: just a pressure switch that, given a pressure above a few psi, makes a contact and sends a constant current through the gauge and then the indication should be steady, just telling that "there is some oil pressure".
Most probably, a ground or similar problem..which explains the rest. Make sure battery ground, engine ground and body ground have solid connections all together. A forgotten ground bus in the rebuilt is a possibility.
Anyway, install a voltmeter in a steady way on the cigarette lighter plug, for instance, and other and verify the voltage. Change voltage bus and ground location using jumpers woith alligator clips to keep the tester connected while the car runs. THis could provide telltale signs...
..about changing the transmission: was a transmission with same code used in the replacement? Wrong code could mismatch speed sender and PCM firmware....but I do not see relation with oil pressure and gas gauge bouncing....
www.avigex.ca/xport/ratio3T40.jpg p.s. this GM chart contains a lot of mistakes however it stresses the meaning of the codes.
