Proper base fuel pressure does make the idle sound smoother for many reasons. You are describing major shaking though. Fuel presssure would not differentiate between hot and cold engines I suspect.

It will do no harm to close the return off though and if the engine runs a little different it means the lift pump filters etc are flowing well enough to increase the pressure on demand. Plus the relief valve was working with an unknown release pressure before the clamp off.

Now if you disconnect the fuel relief line you should get some fuel flow out the line while running. Also submerging that line in a jar of fluid and watching the level increase with no bubbles at least totally clears you of air being present.

Be sure to do that with the engine really warm though as you could be getting air when warm only.

At this time it could be one item or a combination of items.

Back up and start with the valve adjustment. When you come down to hot idle with poorly seating valves you might be partially loosing a cylinder or two. You know your valve clearances are way overdue for a check anyways. This is not unusual in itself.

The exhaust valves for example would have expanded with the heat of the run making any slightly tight valves cold now possibly slightly open hot. In your case you have to cover the basics first. It would only take one exhaust valve having no clearance cold to do this remember. The clearances on the valves decrease with usage and wear over time.