I agree....a challenge! Here are some fragments:
1851 England has 26 Charlot, 37 Charlott, 77 Charlotte.
The only family I can see in 1851 Lincs is in Ulceby, HO107/2118/29 pg 10, "encamped":
Sistance Charlot, head, 30, gypsies, skewer maker, b Cambridge .
Lemontena Boswell Charlot, 26, wife,cabage net maker, b Lester( their spelling)
Joseph Charlot, son,7, b Lincoln Boston
Solenia Charlot, dau,5 ,b Lincoln Louth
James Charlot, son ,2, b Lincoln Lincoln
If you look at Folkingham parish records - a link from Genuki /Folkingham- for your Silvester Charlotte 1827 entry, you'll see it listed as Silvester, bap 1 March 1827 son of John and Sophia SMITH.
No progress on Smith in 1851, though I note an 1861 entry for a Dennis Smith gypsy family in Thorne , Yorks RG9/3525:
"List of persons not in houses":
Dennis Smith,head, 40, cork maker, b Leicestershire
Dennis Smith ,son,20,cork maker, b Abye(?), Lincs
George Smith,son,15,b Kirton
Israel, son 11,b Saxilby Lincs
Caroline(relationship blank), 23, unm, b Bardley
Tennant,son, under 3 months, b Kirton.
There is a UK-ROMANI-L email list on Rootsweb
John