The engine seems to be missing and also making a noise, a little bit metallic sounding and kind of a tapping sound. The sound happens at the same time the engine seems to miss and stumble. When it misses I can see the engine shake a little bit. Noise frequency increases with RPM.

I saw it in person for the first time yesterday and we did the following to troubleshoot it:

-Tightened loose header bolts.

-Pulled, checked and gapped all the plugs.

-Made sure none of the spark plug wires were shorting/grounding to the engine.

-Pulled the distributor cap to inspect cap and rotor and all looked good.

-Used a mechanic's stethascope to try and listen for a loud rocker arm or possbily a bad crank or rod bearing, I couldn't determine where the noise was coming from. If anywhere I would have to say passenger side valve cover.

-Pulled passenger side valve cover, rotated motor over and checked each rocker arm one at a time for something loose but didn't find anything loose.

-While engine was running I pulled one plug wire at a time on the passenger side to see if that made any difference to how the motor ran to try and isolate it to a single cylinder but was generally unsuccesful.

I am wondering if it could be a collapsed or failing lifter? If it was how would I verify that? Any other ideas of what it could be or how to troubleshoot it?

If there is a noise, driving more will cause more damage.  Your description almost sounds like it might be a cam lobe failing.  If that was the case you could adjust the specific valve, the noise would go 100% away but within 20 minutes it will start coming back.

A lobe going flat would be very consistent,  would not come and go at all until you adjust it.  For you to feel a loose lifer the engine would need to be rotated till the valve was 100% up. lifter on the cam base circle to feel the excess play.

Any chance the engine has a broken valve spring??

Maybe start it with the valve cover off to figure this out.  With it running oil will spill, you can make a splash guard out of cardboard for a 1 time use and eliminate almost all oil spill.  With it running take a rubber mallet with a wood handle.   Put the rubber mallet in your palm and the wood end of the handle on the rocker arm above the push rod and push down, a little pressure will make the hydraulic lifter adjust, the engine will miss, then quickly adjust and run smooth.  Take pressure off and it will adjust again.  IF you push on one and your noise is gone you found the problem.  Adjust it and hope the noise does not come back.  If it does come back your cam is already flat and the lifter is cupped out.  Time for new cam and a set of new lifters.  Hope that is not it.