"What we have here is a failure to communicate"- - - - -I love old movie dialog! It shouldn't be necessary to remove the adjusting screws to get the valves to close, unless something else is wrong. The "TDC" mark on the flywheel will align with the pointer twice- - - -once when the piston is at the top of the compression stroke with both valves closed, and again at the top of the exhaust stroke, with the exhaust valve closing and the intake getting ready to open and begin the 4-stroke cycle again. I see in one of the pics that you have the side cover removed. That makes things MUCH simpler, as you can watch the lifters instead of the rocker arms to determine where the cam is in relation to the pistons, rather than looking at just the rockers. I already have a good idea what's happening, and it involves some mismatched parts.
The lifters in your photos are definitely solids- - - -there were never any "milk can" lifters made in hydraulic configuration. There were several lengths of pushrods, however, and engines with the milk can lifters use a shorter pushrod than later models with more conventionally-shaped lifters, hydraulic or solid. It appears you've got early lifters combined with late model pushrods, resulting in being unable to back the adjusters off far enough to create any clearance.
Watch the lifters as you turn the engine over by hand. When the TDC mark on the flywheel aligns with the pointer there will be one place where both lifters are bottomed out. One turn of the crankshaft later, both lifters will be slightly higher in the block, and approximately the same position, vertically. The lowest point of travel of both lifters is where you should be able to set the valve clearance. If the distributor is timed correctly, the rotor should also be pointed toward the spark plug wire for the cylinder where you're adjusting the valves. If you can't get a good adjustment with the lifters bottomed out for each cylinder as the engine turns, you've got a lifter/pushrod mismatch.
Drop me a PM and I'll give you my phone number- - - -these types of discussions always go better in a 2-way conversation than a keyboard marathon!
Jerry