I think the main problem for the Trastamara (outside of the logistics of war and all that) was the lack of male members, at least from this specific Trastamara-Lancaster branch. By the end of the 15th Century only female members were alive, one was Isabella (future Queen of Castile), and the other one was Joanna (alias la Beltraneja). And I don't see the English barons being too motivated into serving a queen, let alone a foreign one.
For starters, you would need for Henry IV of Castile to have more sons and not only a daughter of dubious reputation. With this you made him secure the throne without having to go to war with his siblings (avoiding the War of the Castilian Succession) helping stabilize the situation of the kingdom, while having some extra time to spare with other ventures. Then you could make a second or third son of him to go and present himself as a another candidate for the throne of England when the situation demands it.
Or maybe not his sons, lets say he only has one (the future king), there was still his little half-brother Alfonso. If any, it would be better for Henry IV to help him into gaining another throne just to left him rule Castile in peace.
The other option would be go higher into the family tree and have more sons and less daughters since the start (since Henry III and Catherine's times), but the butterflies would be too big and maybe things could get worse in ways we couldn't predict.