Although simple logic says that the oil pump being on the left side of the engine supplies oil to the left rocker bank sounds good, that’s not the case. For the conventional Y engines, the oil for the rockers for both banks is supplied from the center cam journal. For the LYB engines (368’s included), the oil for the left bank comes from the #2 cam journal and for the right bank, the oil is supplied from the #4 cam journal.
If turning the oil pump with a drill motor, then your oil pressure should be considerably higher. Assuming you’ve already checked all the bearing clearances and they are within specification, then I’d look hard at the oil pump next. A complete disassembly of it and verifying its internal clearances would be easy enough. The problem could be as simple as a stuck open bypass valve within the oil pump. Here’s a past thread regarding the clearances and/or tolerances within the oil pump.
http://www.y-blocksforever.com/forums/Topic22717-3-1.aspx