99 problems and a Ford ain't one.

when you pull the heads, you be able to see the lifter bar interference as fresh metal in an otherwise painted or blackened valley. IIRC your link bars need to be V notched for an LA as straight bars wont work due block casting .As for the sticking valves, you should be able to notice them when you pop the covers on a hot motor and remove the rocker shaft, 5 bolts. All valves should be level and I mean level on new heads! could even take a brass mallet and tap each valve stem to see if it gives. When was the last time you looked at your distributor? Seems the only thing ignition that wasnt addressed in your list of new stuff. reluctor gap can change on a hot motor. very small but maybe enough if your already on the extreme. Should be .008 with a brass feeler to not mask any magnetic drag. Plugs still operational, not all fouled from this, clean them for another test with a wire brush or wheel.

solid rollers should not degrade lift if oil starved (slants will run on no oil for hours at idle, ie Slick50 commercial) but your not as you still have 5psi at idle. do you have a vacuum guage? it will vibrate on a stuck valve. and a slow wander of the needle is a vacuum leak. vacuum leak Can show up on a hot motor as opposed to a cold one especially with Aluminum heads and intake on an iron block. lots of different heat coefficencies (sp?). Get spray bottle of water and start spraying sealing faces and see if idle picks up if motor is still together.
get the right year 383
you need to do an autopsey on the 340 or it's sale value will suck
cut the oil filter open, compression check, do the lifter oil loss check with electric drill and hex while having someone pulling crank around slowly, starter can be too fast
get the fuel pressure under control as 383's need love too
but no reason to risk spun bearings or throwing a rod with micro grit in the oil
actually you may be lucky it won't run
cheers
FYI, you got still got lash on your solid rollers, right? .010/.020 to start if you dont have the specs in front of you.