The air in the oil pressure line will not cause a low reading. It all gets compressed with the same amount of pressure.
I like to adjust the valves with the engine off. Your engine has OEM lifters. They need more turns in than new style lifters. I believe it is 1- 1 1/4 for OEM lifter.
Put engine on TDC #1 and adjust both intake/ exhaust. Feel the pushrod by lifting up and down. When play is gone, give it the required turns. Then turn engine 1/3 of a turn and repeat process on the next cylinder in firing order.
Repeat till done. Only 2 revs of engine.
Put some thicker oil in your engine. You really will need about 30 to be sufficient. On your stock engine.
I usually run 10W-30 or -40 in it. She burns a bit so I sometimes will have to suck it up at a gas station and put in what they have. I try not to do that, though.
Dumb thought: the filter on the valve cover: do they get fouled often? Would that cause a rough idle? Mine has about 3,000 miles on it. I doubt it's the problem but thought I'd ask anyway since two weekends ago there was a TON of pollen down in NC when I was down there. It didn't idle rough until I got it back home.
Is it better to adjust the lifters while running or like you describe? I've done it while running but never tried it your way.