I was about to suggest doing some ignition troubleshooting. But then I re-read your post and the result you got from tapping on the needle/seat doesn’t align well ignition stuff.
Nevertheless, doing a quick spark check during your next breakdown would be quick and easy to do.
I think that’s where I’d start. Reproduce the symptom and try to narrow it to spark or fuel (fuel being more likely).
To verify that your bowl has gone empty for one reason or another. Look down the throat soon after it shuts down. Goose the throttle by hand and see if you can see the squirt from the accelerator pump. No squirt is pretty easy to intepret. Getting a squirt doesn’t necessarily rule out carb/fueling issues, but gives you a good data point to decide on next steps. If I DID get a squirt, my next test would be holding WOT and cranking to see if that clears a potential flood.
It would appear from your pics that we are dealing with a Rochester B. Is that the case? Just throwing out an idea. It’s pretty hard to get the RIGHT kit for a B since the tags are most often long gone. Could be a case of mismatched needle/seat stuff. That’s a spitball at best.
