My dad and I just put a 360 in my truck within the last month. It's a completely new engine. It had the stock tbi fuel injection at first, and now is carbureted. The truck is a 90 w150, previously a 318 truck. We have pretty much ruled out ignition/fuel delivery as a problem, and have installed/tried factory adjustable rockers. There's a brand new cam and lifters in it, and when we swapped the intake, the cam looked in good shape. Is it possible the lifters (stock replacement Johnsons) could be pumping up when oil pressure when the engine is revved up? We are going on 4-5 weekends worth of trying to get this truck to run correctly, and are about at the end of our rope as to what could be wrong. Any and all help is appreciated.

If it's a single pop at the hit it's lean. If it sounds like a continuing popping noise, like a machine gun, you have a exhaust lobe worn off the cam. Pull the valve cover you'll see it as the rocker will barely move.
Doug

Three things come to mind....
Verify ignition timing and phasing is correct
An Intake lobe could be going flat
Or the camshaft is not in proper time

As stated above , cam lobe, also check to see if you have a plug wire mixed up, possible cracked distributor cap? Bent intake valve, broken intake valve spring.

My first guess is it's going lean - especially if it occurs after the peddle has been on the floor for a bit ( upper RPM range). Check fuel delivery first.

If it's a constant pop,, and if you still have an EGR valve on it..look there for sure !!

Egr deleted, stock stamped rockers back on it, timing on cam is correct, exhaust sounds glass smooth at idle and under load, cap/wires/rotor/plugs all new, heads are completely new (redone with new valves/springs/locks/retainers), and 1406 edelbrock carb, just rebuilt by my dad yesterday. This engine did this with the fuel injection on it also, which is why we put a carburetor and old school electronic ignition on it, thinking it might have been a problem. The throttle response is now where it should be, and it is definitely running alot better, just no power and pops through the carb. (not backfire popping, just like its pushing compression back through the intake. My dad has been building engines for the better part of 30 years, and he adjusted the valves when we tried the adjustable rockers, so I know they were good. We were trying to figure out whats possibly wrong, and we thought one or more lifters on the intake were pumping up when the oil pressure is higher, thus holding the intake valves open.....
(sorry for being long winded, just trying to give any and all info so youns get the whole picture)

Do a compression test and a leak down.. see if your
bleeding off pressure to the intake side... but the
spark chases the fuel so its telling you its on the
intake side

We leak checked all 8 cylinders and they were all under 3-4% leakage. It only pops when you rev it up and idle is glass smooth. Like I was saying, we've checked pretty much every parameter of the engine that could be a problem. The only thing that is still the same is the fuel delivery system which is the stock in-tank pump with a mallory adjustable bypass fuel regulator, and it is set to 6 psi at the carb.

It pops hot or cold, temp doesnt matter, and the gauge is liquid filled, but is accurate, we've had this regulator setup on another truck and haven't had a problem with it.

Well based on what everyone has suggested and your response, im betting you have a cam lobe out and you missed it when you inspected it or valves are too tight. I may have missed this in your post but are you running a vacuum advance if so plug it off. May be over timing for your combo.

Exhaust lobe wiped out. Pull the covers and rotate engine while watching rocker arms. You will see if one or more are not moving, or are barely moving. Exhaust can't escape because exh. valve doesn't open, so when the intake valve opens the exhaust escapes into the intake manifold. This is your pop.

There are plenty of known good engine builders that have had camshaft/lifter failures. Lack of good stuff in modern engine oil and/or improperly manufactured cam and/or poor quality cam cores. All though the cam manufacturers won't admit it.