Car Quits At Speed :( stressed

Funny, I had the same situation. Inside of the gas tank was flaking rust. The sock was dry rotted and gone. It would suck rust up the fuel line and fill up the steel fuel filter (which we couldn't see in). It would choke it out. When you stopped, the rust would settle down on the bottom of the fuel filter and it would run until it clogged up again. It took one of those clear glass filter to see it occurring and figure out what was happening. Fix was a new gas tank after we tried to clean it all out and found pin holes in the bottom. Now I'm ok with the old style steel fuel filter.

I had the very same condition in a 63 "Love Bug" VW
When we can kill the battery trying to restart, raise the hood, attach cables and fire it right up... my quarter bet is on electrical fault.