Slant got me stumped

Some ideas and questions roughly grouped in ignition and fuel/carb categories. The compression seems to be good.

IGNITION:
The wrong ballast surely won't help but it is unlikely to cause this problem. Put in a BWD RU19; that will be close to the stock resistances; it'll run better at cold starts in cold weather in any case. Just get this remote possibility out of the way.

Measure the voltage on the blue wire connection to the ballast and make sure it is around 12v.

Find TDC accuately and check to see if the timing mark on the damper is accurate.

Pull the spark wire from the coil; place 1/4" from metal and crank to see if you get a good blue spark. Repeat for a plug wire from the distributor. Don't test across just a spark plug.

Did you change the condenser when you changed the distributor or re-use the same one? That could do this.

Clean the grounding for the ECU very thoroughly, and make sure the ground jumper from the rear of the block tot he firewall is present, is in good condition, and the connections are clean.

What is the plug brand/number? The spark plug tubes should not be any issue unless they are not sealing; I think this year uses the tapered seat plugs with the tube; someone should speak up and verify that; or, you can search this forum for that info.

CARB/FUEL:
What vacuum reading are you getting? Even at this high idle, it ought to be pretty high: 18-22 or so. Does the car have power brakes? If so, has the vacuum hose to that brake booster been plugged to see if that helps?

When you say 'verified carb', what do you mean? What carb is on there now?

What is the choke plate doing? If closed when you start, it should open about 1/8" to 3/16" in the moment the engine starts. Have you tried opening the choke plate by hand
to see if that helps? This will detect an over-rich cold mixture.

How many turns out from fully closed is the idle adjust screw? Usually will be around 1-1/2 turns out.

This possibly acts like the idle and progressive circuits are not working right, and the car only runs well on the mains. But this would be a lean condition, and the plugs would not be blackened by carbon soot.

What specific tests were done to the fuel pump?

Recheck the float setting; does not seem likely for the symptoms, but it needs to be very close. Wet float can be set for the Holley 1920 to see the bowl's fuel level while running (and perhaps others).

How old is the fuel? Bad gas can cause these symptoms.

OTHER:

Watch the valves when running; do some of them seem to be closing more slowly or lazily than others? Sticking valve guides is not uncommon for the /6 and will cause rough running, and can screw up your feel for hot lash settings when running. If you check lash settings when not running (hot or cold) and any are way off, this can indicate sticky valves.