"Move up a grade" is not the answer here. With those clearances, it could run on 5W-20. The issue isn't viscosity. I retract my last statement where I said I don't see an issue. If the OP had 10 psi hot idle with a 5W-20 matching that clearance, I wouldn't see an issue. If the clearance was .0030-.0034" with the 10W-40, I wouldn't see an issue. The fact that it's 10 psi hot idle with .0020" clearance and a 10W-40 is worrisome.
This is pointing to a fault in the oiling system, something like the pump bypass is stuck open or there's a missing oil galley plug. Either case means reduced oil flow to the bearings and top end of the valvetrain. If you go dumping a more viscous oil in there, with an issue like a missing galley plug, you'd be reducing that flow even more.
With the engine idling, check to see if there's excessive oil accumulation in the heads / under valve covers. If not, you'll need to dig deeper.
If I had it, I would pull the pan and check the main and rod bearings, verify clearance, test the pump and bypass, and then pull the timing cover to check the oil plugs.
Again, higher viscosity oil is NOT the answer here. There's an internal fault that needs to be found. I'm iffy to say the oil restrictors are the cause as I've left them out and had sufficient pressure still (with the appropriate viscosity) though it's still a possibility.