I work on a lot of large reciprocating compressors that are built just like engines on the bottom end with shell bearings and gear pumps. Those compressors have oil failure controls that have a thermal timer to allow for oil pressure delay on startup. If it makes you feel any better, those time delays are from 45-120 seconds to avoid nuisance trips of the control and the go 0 to 1750 rpm in a split second, to full load.

Are you using through the pushrod oiling and what rockers? What's the lash set to? I'm just thinking of how much volume there is to refill in your motor when it's been sitting for a while.