Could my 340 block be filled?

Are you talking about the pickup coil in the distributor? Is that something that can be bad and only fail when car is warm and has run for a while. The restarting the car when hot and having no spark has been a solid symptom for a while.
You bet. All it takes is an ohm test when its not firing. You be looking for 350-550 ohms.
I would expect its open or shorted when hot.just throwing parts at it gets expensive. But its not like i can stop by and help you through this. Much as i would like to.