I would suspect the lifters/follower supports. Hydraulic lifter substitutes. They likely are bleeding down after shutdown, allowing clearance to increase, and cause clatter until they are filled back up with oil.
It is not the weight of the oil, it is the check valve in the lifter, or clearance between the lifter internal parts.
One or more will collapse when it it parked with no oil feed, and pushing on a cam support that is opening one of the valves.
You can take the time to inspect all the lifters and maybe find one or more that leak down. The cure is replacement with non-leaky lifters. You would need to apply pressure to the follower as if the cam lobe was opening the valve, and note if the clearance increases, to each lifter in turn. A leaky lifter will bleed down more quickly than one that is working properly. Once you find the leaker, remove the follower, pull the lifter and replace.
You could take them out, disassemble, and inspect for damaged check valve, or attempt to feel loose bore tolerances. Or just replace them all.
I don't think they are $2 items, so it is not as low cost as it might seem at first.
I think I would try to figure out how many were likely making noise, obtain a number of new or used lifters, and check for leakdown. In the shop manuals, the leakdown rate was specified, but I have no idea of the spec. They had a 'arbor press' type thing to apply pressure, equipped with a spring gauge to show how much pressure was being applied, and you would insert the lifter, apply pressure at a given number, and count how long it took the lifter to collapse. Too quick, time for a new one. Too slow, a maybe.
tom