Paul
An excellent question, I wish I knew the answer. From the little pieces of info I've been able to put together, Colt's original design straddled the road. He had originally layed out Rye in 1894-95, steadily improving the links until he left in 1901.
By 1925 traffic became a problem on the road and the club called Colt back in for suggestions. His suggestion was move the road - which was now possible since the club owned the land north of the road, but expensive. So they called in Braid and he proposed they move the course. The committee sat on Braids idea for a couple years and then reconsidered Colts idea, until ultimately calling Tom Simpson who carried out the alteration on the course, creating new holes across the road. How many holes he created I don't know.
According to Hawtree there were complaints about some of the new holes. Simpson's new 1st and 14th are long gone. Sir Guy Campbell modified Simpson's modifications. Frank Pennink - who designed the clubs third nine - gives design credit to Colt and credit to Campbell for most of the numerous alterations, and doesn't mention Simpson.
Evidently in 1947 following WWII they called in the mysterious golf architect Captain H.C.Tippet who had designed Montauck Downs in NY and La Gorce in Florida. The 10th was the last new hole, by whom and when I'm not sure. Even with all the changes I'd think there would be more than two holes of Colt's remaining, especially knowing his connections with the O&C Golfing Society and the President's Putter - but who knows.