Hi Harpraxis,
Like you, I am not entirely convinced of the parentage of William Tyson.
Further investigation of the Nether Wasdale online transcripts reveal the death of a William Tyson of Whitesyke on 19 October 1787. If this is the same William that was born 13 September 1779, then that rules out conclusively Henry and Margaret Porter as parents.
Looking forward to the outcome of your visit to the National Gallery etc.
We will all keep digging.
Tim
Australia