Oil press sure is good, actually a little high the spec says 15lbs at 1,100rpm. Does the noise go away after 1-2 minutes? If so, I found a tsb on pistons making that noise and being similar to valve train lifter ticking, click here.
I read the lifters have automatic adjusters and are not adjustable, cause at first that was a thought. Are you sure there is no oil getting up to the rocker arms and lifters? You may want to remove the valve covers and look. The oil pump produces the oil pressure but the oil pressure is maintained by the bearings, mostly the cam bearings. I doubt the cam bearings are worn since you have 20 lbs of pressure. Perhaps you may have a few pushrods that are clogged and not allowing oil to pump through or a few collapsed lifters or plugged oil galleries.
I would consider using some seafoam engine oil treatment and trying to clean out those oil galleries.
If you do a cylinder balance test and while killing each cylinder you may be able to listen for the noise to change and that may at least tell you which cylinder's valve train components are making the noise.
First of all you will need a 12-volt test light and about 8-12 inches of neoprene vacuum hose. The vacuum hose will conduct electricity cause it is carbon based, use an ohmmeter if you are not sure and see if the vacuum hose you have will conduct.
Now, cut off the same # XXXXX cylinders you have in small equal lengths of the vacuum hose. 2-3 inches will do fine. The small diameter kind like to carburetors, etc will work as long as they fit over the distributor cap tower connection.
Now, mark all your spark plug wires at the cap or coil pack and remove them all. Put those short pieces of vacuum hose on the distributor cap or coil pack connections and shove the other end of the vacuum hose into the spark plug wire boot until it makes a good connection.
Now connect your 12-volt test ground clip to a ground and start the vehicle. With the engine running touch the 12-volt test light to each of the vacuum hose 1 at a time and listen for the cylinder to short out and die and drop in r.p.m. and noise to change.