I have been getting greasy for over 50 years so I thought I heard it all as far as engine noise.
If a rod is bad or an piston related that is under FULL LOAD and you know by the bass sound.
If a valve is tapping it will tap all the time idle or not.
If a valve taps when first start you have a lifter or lifters that have leaked down. This is a TICK not a BANG.
Now for the 03 noise
COLD START (lifter for about 1/2 sec then it stops)
Warm engine (194 deg ) All is fine
Engine under load NORMAL no noise except the exhaust flange gasket.
Engine coasting down hill NORMAL
Now feed it a little gas just cracking the throttle and you have what I hear is a valve train noise.
This is a metallic tick that is on the passenger side only.
WE put NEW Rod bearings in this one about 250 miles ago the guy I get it from said it was 100% out of oil. The #5 and #6 rod bearings where not there at all just all mashed up in the pan.
We replaced the Oil pick up since it was PLUGGED with pieces. Engine temp is perfect 194 to 201 max. NO fillings on the dip stick.
$64,000.00 question what is the noise?
1. Valve lifters are crap from before
2. Push rods, Doubt it compression is to even across the board.
3. Rocker arms
4. Your guess.

 

How's the oil pump itself? They have a tendency to be bad on the 03 trucks.

The other common issue is blown exhaust gaskets. That can make a sound similar to valve tapping.

 

HAS an exhaust leak for sure on the same side as the tapping. It is the exhaust Flange gasket you can hear the backfire when you lift of the gas.
This Noise it at 1825 to 1880 RPM with PARTIAL Throttle, full throttle, silent, off gas silent.
It might just be a harmonic at that RPM.
Oil Pump is new did that when we did the rod bearings.

 

One other way to get a noise like that is backflow through the SAI system due to a stuck SAI valve or bad solenoid.

Also this issue may cause a low frequency burble at idle, which may not be noticed without opening the hood.

Just a thought.