just sounds like its getting old and tired to me, bearing clearences are getting larger, when its cold the oil is much thicker, so you have better pressure..
It could also be a pressure releif valve stuck open, but usually with 2h's the get stuck closed, who knows, might be worth investigating, its located on the timing cover, drivers side, theres what looks like a bung there, once unscrewd theres a spring and cylindrical valve.
If you do happen to remove it have a drip tray underneath as oil piss's out. Also be preepared for the bung to fly, its spring loaded so be ready to catch it. the pressure releif valve will want to stay in the hole, i use a bit of dowel to stick in and remove. Have a look at the piston, its more than likely worn on one side, this allows the piston to cock over and jam...but like i said, im more leaning towards the fact its possibly done a few miles and the engine is getting tired. Id be inclined to put a proper pressure guage on first and actually see where the oil pressure is, if its staying above 40 to 50psi i probably wouldnt be concerned