Well now, looking at the map one cant help but notice several groups of stopping places
To the south of Grantham, there is Skillington, and Castle Bytham, on the road towards Bourne. Moving northwards to Sleaford, we find Scredington, Ancaster, and Heckington
Moving north of Sleaford we find Leasingham, Kyme, Billinghay, Navenby, Metheringham, Coleby, Harmston, Dunston and Potterhanworth, Hykeham, Branston and Eagle as we get close to Lincoln.
North of Lincoln we find North and South Carlton, Burton, Springthorpe, Scampton, Corringham, Blyborough, on the road to Scarborough.
If we go back to Lincoln and move north east towards Market Rasen we find, Nettleham, Langworth and Lissington.
If we were to assume that the travel north of Lincoln was making a route to Brigg fair, and returning south by the other route, that would make sense. A popular stopping place with a lot of Romany baptisms is Wrawby a village by Brigg.
To the east of Wrawby is Melton Ross. Moving north again towards the Humber estuary we find Caistor, Winteringham Wootton and South Ferriby. Louth actually remains rather isolated to the right of Market Rasen.
South of Rasen we find Horncastle, once known for its Horse fair. In the vicinity we find Ashby, a village known for Romany settlement, like Kyme.
Directly south of Horncastle, is the hamlet of Brothertoft, near Boston (another town known for its romany settlement). to the west of Boston we find Kyme and Heckington..... on our way back to Sleaford.
If you follow the map you can see the routes they took, most likely moving into Leics and Nottingham through Mowbray and Newark along the way.
Regardless of surname, all the places mentioned have at least one romany baptism/marriage known to me.....