Peter,
You really have to drop the tank & sort out why crap is getting through.
I have had this as a student in a Hillman hunter and used to carry a foot pump to pump the crap back to the tank from the engine side . However it always returned.
I also have a vintage Swift that did this-and cut out like you said. The motion must be mobilizing fines & clogging the line.
You may get lucky by draining the tank & starting afresh.
Frost do a slosh kit that should fix the issue if you get the tank out--I have used it in my Swift & a friend in an AC Ace and it works.
POR-15 Car Tank Repair Kit | Frost Auto Restoration Techniques
Graham