340 issue after camshaft change

Lash Caps?
Pedestal rocker bolts can break with an aggressive cam, strong valve springs and the aggressive driving that goes with the previous two. That is the reason the OP has 7/16 7/16 studs. Adjustable push rods and lash caps get you back to the same situation this started with.
The OP needs to go through the motions of pull the intake off to visually check lifter status regarding off base circle and plunger travel position in the lifter bodies when the valves are on the base circle. With the intake off and a piston at TDC, it is easy to verify if it or its running mate are on the base circle. Those lifters will be lower than the running mate which will be on overlap and both lifters will be raised a bit. If the lifter bodies are both low but the valves are off their seats, back the adjustment off to get clearance like a solid lifter cam and then do the one finger zero lashpoint adjust. Then tighten down the adjuster nut 1/4 to 1/2 turn to set the plunger part way down in its travel.
Working with running mates and adjusting the cylinder at TDC firing has always worked for me.
You want sensitive adjustment, try 12V or 16V Detroit Diesel timing that uses timing pins of various lengths for different injectors, or a 2300 Cummins V12 with Top Stop injectors.