Hey Jason,
My Polson research is predominately covering those families that lived in Chesterfield Co. or at least started out there. I know that Jeremiah Sr (born around 1780) and Jeremiah jr's, born around 1805, descendants ended up populating the "Polstons" in Marlboro Co.
Jeremiah sr and Jeremiah jr. are listed in the 1839 election return of Chesterfield County.
The Jeremiah, born @ 1805, is listed in the 1850 census for Chesterfield District but sometime after 1850, I believe he moved to Marlboro Co. because that's where his descendants are listed in subsequent censuses.

I have been to the cotton museum in Bennettsville, Marlboro County and they have some very good gen. records.
I've also been to the county courthouse in Bennettsville and found there was David Polson who died in 1868. He had two brothers; Jeremiah and Levi. I'm guessing, this might be the Jeremiah jr. that I mentioned earlier. Levi was the executor of David's will.
Since David did leave a will, you could probably contact the courthouse and get a copy of it. It is indexed by"Apartment #49, package #9."
Another David Polson that I have info on was born Aug 10, 1847 and died Sept 26, 1925. He is buried in the Polston cemetery in tatum SC.
The third David Polson I know about was my g-g-uncle born @1841. His common law wife was Rebecca Perdue and they raised their family in Darlington Co., although his brothers and sisters remained in Chesterfield County.
Just speculating-- Maybe your David Polson was Jeremiah jr's brother. If that's so then Jeremiah sr. could have been his father. I am in contact with a researcher that has been told the Polstons were from Maryland. She has records bearing this out and a Jeremiah Polson is listed in these records.

I also have info from a 1766 petition for a land grant. The petition is from Jeremiah Polson who requested that a reserve ...of a quantity of land on the River St. Mary be set forth for some Bermudian Families he in consequence thereof was desirous to remove his family into the Province[Georgia], being a wife, 5 children and 4 negroes. Granted that the land prayed to be reserved for six months."

Thanks for the contact, Norma