Well, this is a weird one for sure!
Did you have the low-oil pressure problem before the rebuild?
Any exterior oil leakage?
Any evidence of oil in the coolant or coolant in the oil?
I think changing the weight to 10w60 will only mask the real issue.
So, let's think about how the oil system works. The pump sends oil up through the block to the oil filter manifold, through a check valve, and then through the filter. That oil flows to the main bearings and up through a passage in the block through non-return valve (another check valve) and on to the VANOS solenoids, timing chain tensioner, and the moving pars of the cylinder head, tappets, camshaft bearings etc. The oil pressure switch is in the upper end (end of the line) in the cylinder head. So, any restriction in the system could cause the pressure to rise (before the restriction), and drop (after the restriction). Your above idle pressure seems low too. After I changed my oil pump, I check the pressure, and I had 48 PSI above idle. 2.6 bar is 37.7 PSI.
I'd pull the non-return valve (connect a hose to the port), disable the ignition and fuel system, and crank the motor. This would be to flush any contamination from that passage. Then I'd put in a new non-return valve. If the non-return check valve isn't opening when the oil pressure hits it, you would have reduced oil pressure to the VANOS solenoids, timing chain tensioner, cylinder head components and the low-pressure switch. Recheck your idle pressure after you change the non-return valve. If it's still low, I'd look to the the check valve in the oil filter housing. However, the check valve in the oil filter housing is a bypass type. It only opens if the oil filter is clogged, allowing oil to flow in case of excessive filter contamination.
BMW Cylinder Head Oil Check Valve - Genuine BMW 11367537692
www.fcpeuro.com
Oh! And I know this is the obvious point, but what is your oil level on the dipstick. Not to be insulting of course.
