Well, I think it's solved. PackardV8 suggested on this thread to open the point gap to 0.018". The Repair and Tune_Up Manual for the 23,22 and 21 Series has a page that says the point gap should be between 0.0125 and .0175". The Tune-Up Specifications and Adjustment Chart for 1949-1950 says .017" for the IGT 4203 Autolite distributor that I have. When I replaced the points about a month or so ago I set them to 0.016", which was a compromise and a number I remember using for all the old eight cylinder cars I'd owned in the early '60's. So anyway, I thought what the Hell, I'll open them up to 0.018. I did so and ran it and it was a bit worse. So I figured if opening them up makes it worse, then what will narrowing the gap do? After all, the one tune-up guide said I could go all the way down to 0.0125. So I incrementally brought the point gap down and lo and behold it ran better! I finally settled on the lower bound (0.0125") and it ran about the way it should, although it was a little sluggish (but no rough running), but I suspected the timing would be off a bit due to the point gap change, and indeed it was. So I advanced it a bit, back to spec. I haven't yet tested it, but I think it'll be fine now. My question is, why is it so picky? I've never owned a car where the point gap mattered that much. If you were within a couple few thousandths of 0.016 you were fine. When I set the points I move the crankshaft by turning the fan and I'm pretty good at getting the point cam follower right on the peak of the lobe. So I don't think it was an issue of not setting the gap accurately.
Anyway, I'd like to thank everybody who took a shot at this, you were all very helpful and I appreciate your help.

I checked the manifold heat riser valve and it moves freely. I did consider the possibility that an internal piece of the muffler could be jammed in such a way that it restricts the flow, but I have no way of testing that hypothesis, short of removing the muffler. And I'm sure it's probably rusted on to the exhaust pipes so it would have to be a job for a muffler shop. It may come to that I suppose.

Oh, and the fuel pump is brand new from Max Merritt. It was a little different than the original, but Merritt says it's correct for that car and it fit fine. I approached this incrementally, replacing one thing at a time to see what the affect would be and changing the fuel pump did nothing.

It happens whether you're in motion or not. On the road it occurs in second gear (not yet in overdrive) at about 35 mph. In third gear (out of OD) around 50 or so. It really sounds like it occurs at about the same engine speed each time. When I rev it in neutral in the garage and look down the carb the main nozzles seem to be spraying fuel ok. When I look way down the throat I can see the throttle valves and they don't seem to open up completely until the last couple of inches of pedal motion, and that's when the engine starts to lose power and run rough.

The cables are copper core, at least that's what it says on them. And they look pretty new, although they have little lumps in them which I thought was odd, but I took one off the number one cylinder and watched the spark jump when I held it close to the head. I just figured they were fine.

Yes, I checked the float level and the metering rods appear to be functioning as designed. There's not much to that carb and I've looked through every little passage I can find to make sure everything is clear.
Regarding the ignition, the centrifugal advance seems to work since the timing mark advances when I increase the engine speed with the vacuum advance disconnected, it's just that the little hand test of the breaker cam doesn't seem to move the way it suggests it should in the documentation. Is it hard to remove the breaker plate? I'm not sure which screws to remove. I know I have to remove the vacuum advance mechanism, but what else?
The problem (rough running) occurs when the pedal is almost to the floor and the revs are pretty high, much higher than the 1800 rpm where the max mechanical advance of 12 deg occurs for the IGT 4203 Autolite distributor, so I guess it can't be ignition come to think of it. I'm really at a loss as to what's going on.

in the document you referenced they describe a simple test of the centrifugal advance by turning the breaker cam. I can turn it but it doesn't turn very much, maybe a few degrees, feels just like slop in the drive gear, is that correct?

Hey thanks It has a lot of good stuff in it. I have most of the applicable documentation on my Packard but I must have missed this one.
I'm still struggling to figure out what's wrong with my '49. I took apart the carb for the umpteenth time, trying to see if there's something obviously wrong, but everything looks ok to me.

Thanks for pointing that out. It sounds like that other guy had the same problem. However that cap screw seems to be secure on mine. I think it's a half inch hex and I couldn't move it . Also the distributor is not moving when I try to turn it with my hands.

Yeah, I see where there's some slop (not as much) on the distributor on my '50 Ford. Well, at this point I'm really grasping at straws.