Hi Jule, I see that this is an "old" query - are you still interested in a reply and corrections about your husband's Gleason line?My gggrandfather was a Dickinson so I have quite a bit of information regarding both surnames.
Thomas Gleason, b. 1607 was born Thomas Leeson.He and his Puritan family immigrated and lived in Watertown/Cambridge, MA for many years before changing his name to Gleason.Therefore his parents whomever they might be were named Leeson - not Gleason.The name Gleason was not an English name and any Gleasons in England in the 1600's were probably immigrants from Ireland. Even in Ireland the name Gleason was usually spelled Gleeson.
There is no real documented information regarding the parents of Thomas nor his wife Susannah Page in England.However, we have proved that Thomas was directly related to the Stotesbury-Leesons of Sulgrave, Northants, England through DNA testing.Unfortunately, DNA does not provide the exact identity of his parents.
I have some information on all of the descendants in your husband's line down to the last Moses but nothing more recent or even a connection to David.