Carb King will probably weigh in again soon on this one but in the meantime I'll do a thought experiment informed by a good bit of experience.
We've eliminated fuel pressure and delivery. Have we eliminated retarded timing? I may have lost track. That said, it is not safe to assume that because the carb was rebuilt recently that all is well in that department. Things change. Grit comes loose when you're mucking about and ends up where it shouldn't be. Screws come loose. Vacuum sucks gaskets in where they're cracked. Heat warps metal. Nuts holding carb to the manifold work loose, etc., etc. Bear in mind that you may have more than one problem simultaneously.
Your plug reading shows it running way too rich. No news there. Is that from idling or running down the road and quick shut off (plug chop)? If it's just from idling then there is excess fuel feeding the idle circuit for some reason. If it's from running down the road perhaps fuel is siphoning into the main-jet discharge tube for some reason; loose main jet? Again, you may have more than one problem. Is this a W-1 Carter or a YF or something else? If a YF, perhaps the accelerator pump has succumbed to ethanol. But then you say it obviously squirts when it should. If it's a Rochester B there are all sorts of problems associated with warpage and pluggage that I'm not competent to comment on.
I'll chase down the generic lean-mixture-off-idle problem.
Usually a stumble on throttle opening is caused by a lean condition or retarded timing or both. It idles normally, you say at about 1-1/2 turns out on the idle screw? But wants to die when the throttle is opened? as though something apparently starves it of fuel when it comes off idle. Or, perhaps it's idling too rich and then starves for fuel as soon as the throttle is opened?
On most carbs, there are two tiny, tiny ports in the carb throat, one above and one below the throttle blade when it's at idle position. The one below is the idle port which is fed through the idle mixture screw. The one above is the "transfer port" and provides extra fuel (and on some carbs a fuel/air emulsion) as the edge of the throttle blade moves above it, exposing it to vacuum. If this transfer port is plugged with a tiny bit of grit, the engine will idle normally but stumble as the throttle is opened. One is tempted to compensate for this by advancing the spark or enrichening the idle mixture or both but then it idles too rich and pings on acceleration and you still have a stumble off idle.
If there's a vacuum leak at the manifold flange for some reason, you'll lose the vacuum signal to the power circuit and it'll be rich all the time except at idle and the vacuum will be low off idle and the transfer port will not suck enough fuel. If the vacuum passage is plugged with gasket cement or whatever, you'll have a permanent rich condition as the power valve will be open or the metering rods will be up, depending on carb design, but the transfer port should behave normally.
Fixing the transfer port problem may not be easy as you can't get an air nozzle into the carb throat easily. Try pulling a bristle from your wire brush and use that to poke into the transfer port. Then use an air nozzle that has a long tube you can bend and squirt air into the port. Finally, blow air from the other end and put your thumb in the throat to feel if there's an air jet coming out.
This is all a lot of trouble so check that all the carb parameters are correct first, eg. float level, float drop, float jet size, correct size check balls in where they should be, gasket integrity, air-horn warpage, loose screws for secondary venturi, (if any) warped accelerator pump diapahram retainer or loose screws there (if any).
My best guess is that you have two problems: 1) High float level, perhaps caused by grit stuck in the float valve. 2) Blocked transfer port, again caused by grit. A third possibility is that you have turned the idle screw out to compensate for the off-idle problem and that is the cause of the rich plug reading and you still have the transfer port problem.
I'm hedging my bets here because it's really hard to troubleshoot remotely where I forgot what somebody said several posts ago.