Not too familiar with the upchannel area but Dunster itself looks like a likely spot on the flood. Minehead is good from the shingle beyond the harbour on the flood, casting out towards the concrete structure offshore (Gasworks beach).
Bossington is very good, park in Bossington itself and walk down or risk your paintwork/undercarriage on the farm track down to the beach. I've generally fished towards the point at the head of the beach, but if spinning is your game think also about the flood into Porlock Wier or the ebb at the breach in the shingle bank. Porlock Wier from the shingle is OK too, there's clean ground for long casters. My experience in general of the shore fishing was that you need to be a very competent caster, local knowledge (old smoothhound?) will be worth its weight in gold. I gave up trying years ago-boats are more fun
Lookfar will be in and out of Porlock Wier next week and the week after for two hours either side of high on calm days. Say hello and if I'm not already fully crewed with friends and family you can hop on for a mackerel bash, or whatever we are up to that day.