If you still have problems after you try it yourself, send it to PapaNick in Ny. He does a nice job and is very reasonable. He usually advertises in the ads section.
Once while watching Chasing Classic Cars, Roger the old mechanic let it slip that MMO was their "secret juice" they put in the cylinders to loosen engines that have been sitting for a long time. Seems to work for them.
I put a small shutoff valve right near the carb and I shut it off and let it run out of gas when I'm parking it for a while or putting it in my attached garage. Works good for me. I don't use the one inside the car.
I had the exact problem. I thought it was the water pump or the altenator. Just for the heck of it I sprayed some belt dressing on the belt and it immediately went away!
Check and see if the bolts are loose holding the carb to the manifold. I just went through the same thing and the bolts were loose. Also if your running a tilitson carb, make sure it's not warped at the manifold.
I went with the rebuilt one from Snyder's. You exchange your old one. It's a little pricey but all you have to do is bolt it in. I didn't need to adjust mine after install. I have replaced them on both of my As with them and I'm totally satisfied.
I just saw on another site that they are back in business. I bought a used one and they are great for working on our cars. Much safer than jack stands. Also they are still made here in the US. It's great to see an American company come back.