Sorry Rick, I don't know anything about the Independant Companies. Where was George Green born? There were a LOT of George Greens.

Royal Hospital, Chelsea: Discharge Documents: WO 121/60/191
GEORGE GREEN Born WAKEFIELD, Yorkshire Served in 26th Dragoons (Light); Hull Invalids. Discharged aged 40 after 12 years 8 months of service . Certificates of service (disability or reason for discharge, length of service, rank, regiment, age, place of birth and trade on enlistment).
Date: 1802

Royal Hospital, Chelsea: Discharge Documents of Pensioners WO 121/188/513
GEORGE GREEN Born [Not Known] Served in Independent Company; 26th Dragoons (Light); 5th Royal Veteran Battalion Discharged aged [Not Known] after 25 years 10 months of service Original certificate of discharge missing. Residence or place where pension paid stated in document.
See film image 933
Date: 1816

From what you wrote, this last one was the GG you are looking for. (Or was he discharged both from the 26th Dragoons, and later from the 5th Royal Vets?) Did you read through all the documents above?

Sue