all valid ideas to try,, the problem is now it becomes swap parts until you find the problem.
I'm no fan of the PetIII ignition system either, the Tach signal that comes off the PIII is a Square signal and it will not work with the factory tack. i've seen it do some weird things as well.
I went back to the PII because of the automatic dewell adjustment to help with startups.
I would agree the engine builder should be helping you, however my experience is those guys are usually scum after they get your money.
you can inspect the coil for obvious issues, for example I had a new MSD oil filled coil i put it and went for a spin, it didn't run right. when i came back i had oil on my intake that made no sense. turned out the oil inside the MSD coil designed to help keep it cool was leaking out through the top. the thing was basically defective out of the box.
could be a cam issue but the smoke is saying combustion gas is getting into the valve covers.
your plugs are fowling with fuel as well, that is saying ignition issue or a combo of unburnt fuel and oil fowling the plugs.
i would 100% regap the plugs to .35, then reset the initial timing, disconnect the vac accessories if you have any plug the vacuum connections and see what the vac readings are.
you could have a vac leak, but smoke coming out the valve covers would indicate combustion gas coming out of the valve seals.
ignition issues can mask as a valve issue. i suspect you have 2 issues, ignition and the valve stem seals or valves themselves.
you can run on bad valve stem seals what will happen is the plugs will get some oil fowling and you will consume oil as the stem seals get worse it will consume more oil and eventually the car will smoke at start up from oil getting into the cylinders.
What gets me +-2"HG flicker you see on the vacuum gauge.
check out this site
http://www.secondchancegarage.com/public/186.cfm don't go crazy if you see similar HG readings on your engine it is more of a guide to point you into diagnostics.
now there could be other options like poorly seated valves. that is possible since this is a new rebuild the machine shop could of screwed up the heads.
the valve springs could of also be incorrectly setup or tensioned that would require rocker adjustment again possible for a engine rebuild where the builder messed up. if the builder setup the rockers loose because he was suppose to make adjustments later and he forgot that is an issue.
a bad electrical problem will also look like a burnt valve or a sticking valve on the vac gauge.
your compression test sounds good, if the valve was not fully closing on some of the heads then the compression readings would be all over the place indicating a problem.
i'm leaning towards problems with the heads on the engine with the stem seals.
The best would be to try and get together with the engine shop. if the car is drivable then take it over to them and explain the problems and let them look it over. you have a new engine so its obviously not right and they should be at least willing to help you and diagnose it.
the other end is going it alone and swaping out parts and trying to narrow down things. but again i suspect 2 issues that are overlapping a little. ignition is showing a problem on the plugs and smoke from the valve cover vent is showing a seal problem.
also changing the coil would be a good test.. since after 5 minutes it loads up and dies that could indicate a bad coil as well.