I'm gonna throw out a few more questions here.
1) You said you weren't running a PCV valve? Why the heck not? Running without one would be enough to make a new Honda leak oil!
2) This is related to the first question, and has been asked before. Do you have a baffle? Most aftermarket valve covers fall into the "if it dont go, chrome it" category. If you can see rocker arms through the PCV hole, it's gonna suck oil. Try putting the factory valve covers back on to see if the smoking goes away. Besides, unfortunately most guys today have no idea who M/T was. Too bad that.
3) Are you leaking/sucking oil internally? You might be pulling oil from the lifter valley, especially if the heads were milled. Here's the deal, running 360 heads on a 318 requires a pretty healthy cut to reduce chamber size. (What was the chamber size anyhow, your builder SHOULD know this, and should have provided you with such data, THAT is how you determine compression ratio). Now, if the heads were cut on the deck surface, the manifold face needs to be cut as well. If it was not cut, or cut the wrong amount, the manifold will not seal well. If the heads get cut any amount at all, DO NOT use the rubber/cork end rail gaskets, just RTV, or the manifold may not fit at all. You builder should be able to tell you EXACTLY what he removed from each face.
Anyhow, here's how to check for vacuum leaks into the lifter valley: Start engine and cover the crankcase breather inlet (and/or oil filler depending on your valve cover design) and allow a vacuum to develop in the crankcase. If the idle speed changes or smooths out, you have internal vacuum leaks. If the crankcase will not pull a vacuum, you have a PCV problem, or haven't sealed all the vents. If there is air "blowing out" of the breather, you have trashed rings and there is no way to ever make the engine produce power.
4) I would be really suspect of any shop recommending 20w50 for a street engine, especially if they tell me it is to "take up" clearances! Just what were the bottom end clearances anyhow? These should be on the same "builders notes" page with the chamber size, piston deck clearance, head cuts (and associated custom pushrod length) that the builder gave you with the engine. Your builder did give you such data right? They did measure things right? Clearances and leaks are not the same.
Thick oil IS NOT always a good thing. It takes A LOT of power to pump, flows like crap, drains back slow, is hard for rings to control, etc... 15w 40 is about max, and 10w 30 is probably better for streeet use. Look in you owners manual and see what MOPAR called for. Face it, these engines ran long periods of time using the oils available in the 70's and 80's. Lubricant technology has come a long way since then. Compare todays oils to the best oil available when these cars were made. You simply can't buy oil that bad today.
It sounds like you may have a few things going on here. AVOID SHOTGUN MAINTENANCE!!! Work one issue at a time. Make one change, evaluate, take notes, etc. If you change more than one thing at a time, you will never know what the problem was (or if you fixed one problem and created another).
Oh, and DO NOT under any circumstances try to dyno a smoking motor! I would not trust anybody who would put a smoking motor on his dyno. (Unless I was getting a cut of the ticket sales for the "exploding motor show") It takes very little oil contamination to send an engine into destructive detonation (think Diesel), far less than is required to make smoke.
White smoke might mean water. Is the water level going down? Does the smoke stop if you loosen the radiator cap to the "pressure relief" notch?
