Just a thought, but after you packed the pump with vaseline, did you prime the pump manually before you started it? When I put my 360 in, I packed the pump with vaseline, then made a tool which slid into the distributor hole on the timing cover & engaged the oil pump. I used a variable speed drill to turn the oil pump & prime it up. I haven't had any oil pressure issues. Just something you might want to try.
1983 CJ7 AMC 360, T-5, Dana 300, Dana 30, AMC 20
Warn XD9000i, RE hand throttle, 1" body lift, OBA