John Dodge - Evidence for parents?

What besides FamilySearch (unsourced) supports brothers (?) John Dodge & Isaac Dodge of East Coker in Somerset as son of Oliver Dodge (of Stockport in Cheshire??) & his wife (was she?) Hannah Agnes Dodge of the (fictional) location East Coker, Yeovil, Somerset, supposedly a daughter of Robert Lambe of Leeds in Yorkshire?

The Dodge Genealogies seem to show them living in various places in England, but the Somerset branch leads to the Massachusetts Bay colonists, Richard Dodge, of Dodge Row & "Farmer" William Dodge, of Beverly And supposedly the Dodges of the East Coker area were there since the Great Plague (1349). However, the first parish registers are not until 1560 at best. (See notes in profiles for Capt. John Dodge, II).

So how do we support this Oliver & Agnes?

Or do we disconnect them?

Thanks to jeffrey gorton for asking questions - even if he may not like my answers. :)