I've been thinking about this some more and trying to find actual evidence.
The burial of William Dodge 4 Jan 1845 in the Halstock register gives his age as 84. (born 1761)
https://www.opcdorset.org/HalstockFiles/HalstockBurs1813-1912.htmThis fits with his age on the 1841 Census.
The will of William Dodge proved 28 Nov 1845 of Liberty Farm Halstock, (on The National Archives), gives children Simon, William, Joseph, Martha (married), Julia( married), Susan (married), Sarah (married), Anne, John and Elizabeth.
You can see all their baptisms on freereg. mostly baptised at Closworth.
Although not mentioned in his will of 1845, another of William and Mary’s sons was
Samuel Tasell Dodge, baptised 4 Jan 1786 at Closworth, (on freereg.org.co).
Perhaps he had already had his inheritance, or they had fallen out when the will was written.
There is also a will of William Dodge 10 July 1816 of Closworth, Somerset. He has children William, Elizabeth, Alice, Sarah, Samuel and Mary.
He has land at Closworth, and at East Coker (3 miles north of Halstock).
And Closworth Somerset is 2 miles over the border from Halstock Dorset.
His son Samuel was baptised 15 Jun 1778 at Closworth, father William, mother Elizabeth.
William Dodge married Elizabeth
Tessell 23 Nov 1759 at Closworth.
So this is the generation before William that died in 1845.
The William that died in 1845 was the son of the William that died in 1816 - so not father Solomon at all.
This document from The National Archives would seem to confirm this, - an exciting find. It would be worth sending for a copy I would think.
https://discovery.nationalarchives.gov.uk/details/r/96abcca6-1dcd-48e0-b070-9b3dac57c048There are several Dodge families around this part of Dorset/Somerset at this time as you have found.
The William son of Solomon wasn't born until 1764 - a possibility, but the other William, son of William, is a much better fit given the documented ages, even if there wasn't the very strong evidence of the name Tassell continuing through the 2 families, and the document at the National Archives which gives Samuel Tassell Dodge as the grandson of the William of Closworth who died in 1816.