On my 99 xlt 5.4l. I have a tap on the passenger side that sounds like a valve. I have done allot of listening and looking to find that mine comes not from the valves, but from the first bend on the exhaust manifold. When the engine warms up it will " echo " the sound of the internal pop. Odd.
As far as the bad running. The worst case is that you may have to rebuild that head. Though this idea always causes a problem for me. If I am doing one head, it would be worth while to do the other side, and if the engine had 200,000 plus miles, and is a stock/factory engine. I might was well just rebuild or buy a new. This can be a big price tag. Looking at some built engines with up to 300hp and a option of a super charger intake system.
I would look into sensors that run that side. The MAF, I think, would make the whole engine run funky. A plugged injector would make it run crappy. Check fuel pressure.
What kind of fuel do you run. cheap as you can find from the cheapest station, that only gets new fuel once a year. Do you run a mix of different stores, IE mavrike, chevron, texico, 7-11, etc. These have different fuel additives. I would think that running the same fuel from the same store would be a good thing.