This is interesting. I read the Kent New Romney Dragoons history too. I had assumed my 4 x great grandfather was a regular, not a fencible, but I cannot find any records on Findmypast. I have also tried various spellings of John Foreman but have come up with nothing.
I therefore think he was in the New Romney Fencibles, as he was born in the New Romney area (Burmash), with the New Romney Fencibles possibly stationed in Beverley East Yorkshire - or somewhere not too far away. I think East Yorkshire has a strong connection with dragoons but I am no military historian.
Also, around 1800, things were still quite hairy from a military point of view so I understand the fencibles would have been stationed all over the country.
"For most, 1800 was a terrible year, hardly enlivened by the visit of the Russian general, Arbeneff, and his inspection of the huge militia force which was still thought necessary to keep in Hull ---- the third West York Militia, the East Sussex Militia and the Sussex Fencible Cavalry." - P 238 A History of Hull by Edward Gillett and Kenneth A. MacMahon, Hull University Press, 1980 ISBN 0 85958 448 8.