Sorry to hear the fuel pump rebuild didn't do it.
Let's see, the low speed passage is up there in the plastic top, and probably other vents that could have been blocked with a bit of epoxy, or the mend wasn't complete. Don't seem to have an idle problem, but carb venting could be an issue. (The top assemblies appear to be available at about $70 or so.) Think you hadn't run the motor much before, so might not be able to tell if there was a preexisting problem (carb body repair). If you have never run the motor successfully through mid range, wouldn't rule out that earlier repair. But would look elsewhere if the problem came up suddenly.
You might try to replicate the stalling or stumbling, running in a barrel. With a timing gun, you could check to see if spark is cutting out when rpms are advanced. Works for dropping one cylinder, of course. If the engine is stalling for sudden loss of spark on both, test wouldn't help (ain't a whole lot of spark generated if the engine flat out quits -- just doesn't help much to know spark stopped at that point.) You are then into testing or replacing ignition parts. Standard spark testing with a tester is always a good idea, of course, but chances are you will have good spark when testing. (I think I would do it anyway, just to be sure.)
If up for some CD ignition testing, there is a good site that is often referenced:
http://www.ebasicpower.com/downloads/cditech/CDI-Troubleshooting_Guide.pdf
I've had a little success with testing, but honestly would not have solved problems on my own stuff without swapping out parts between motors (and I still ended up with an extra working power pack, when I was absolutely sure the unit was bad).
