It's funny where you find cousins :):):). I'm related to the Barons/Earls de la Warr through Thomas West, 8th Baron de la Warr (of the 1st creation, 1299). Two of my cousins married into the family. Firstly Lady Eleanor Percy, though she never bore children, then secondly Lady Elizabeth Mortimer and they had 6 children. Your Thomas is his grand nephew. His grandson, the Governor, is his great grand nephew (g-g nephew). You most likely trace your Plantagenet in the de la Warr line through Eleanor and Elizabeth...although you may have others.
Actually, if you'd like to know, you still have cousins of the de la Warr's running around....the present 11th Earl de la Warr is William Herbrand Sackville (West).