Need help with the 3.7L

Your symptoms do indeed sound most likley to be fuel system related at this point. Since you ran out of the jug and it did similar things as on the road, then it does seem that you have isolated the issue to not be in the tank but keep in mind that crud from the tank may have caused the problem in the first place. There have been oodles and oodles of threads on this problem and the old tank is the most common issue.

If you have the fuel pressure gauge, tee it into the line just before the carb and see if the pressure is steady at idle and on up to the problem RPM's. Or just put on the new pump and see what happens. Beyond that, it could only be the carb (if the diagnosis of a fuel problem is right....).

The heat flapper would not cause this by itself in general. But the other possibility is that this a cold driveability problem. Was the engine fully warmed up when you tried this? I have had a similar problem when the engine was not fully warmed up, the choke was pulled off (I have it set lean), and it just would bog and stumble at above 1500-1800 rpm in the first mile of driving or so. But it would warm up fast and go away in another half mile or so, so this is not likely your issue.

One other idea: At what gap did you set the points in the distributor? Did you change and set them, and change out the condensor? If you have not done that, go back and do that first, as you have missed an important part of the ignition system that can cause severe driveability problems when bad/set wrong. (Sorry I did not re-read your initial post sooner and catch that you did not mention them being changed.)