I'd put on an oil pressure gauge and watch how long it takes oil pressure to rise. There is a chance the oil filter is draining out and it takes that long to build pressure. Some engines have an anti oil filter drain back valve, not sure if these do or not.

At least on my 97 M104 inline 6 , when the oil filter cap is removed and filter element extracted, the filter housing drains out. I'd have a hard look at how that system works to make sure it isn't leaking when the filter is installed.

If your timing chain guide rails are not worn / broken, I'd be real tempted to put something in / on the oil fed tensioner to limit how far it collapses and maybe a light compression spring. You could set if up so the chain is slightly loose without oil pressure rather than the drastically loose you have now the nose will be greatly reduced.

Many cars of other brands use a ratcheting mechanism to limit collapse but I don't know if these cars have them or not . ( apparently not due to the start up noise. )