I think your on the right track with removing the valve. Maybe just drill out the center and use an easy-out.

I have an 87 P'up, and the carb was replaced with a new/remanufactered unit just before I bought it, I rebuilt it twice, cleaned it twice, adjusted the float numerous times, and still every now and again it runs like crap for a few days. Just like you describe. I think it has something to do with one of the electric solonoids on the carb. Or the common idea that the carbs are crap.

I had an 85 that was the same, untill I replaced the carb with a Weber I scored on Ebay.