Well, would Henry VI still be Henry VI? That's a pretty strong butterfly net you've got there, even when you give the caveat of Bolingbroke overthrowing Richard II. If the PoD is between the birth of John of Gaunt and Edmund of Langley, then loads of stuff is up in the air before Henry becomes Henry IV.
Without Thomas of Woodstock, Duke of Gloucester and the Lords Appellant, Henry may never be exiled. How do we know the Black Prince will die on schedule?
It's an interesting idea, but there are an awful lot of divergences before we get anywhere near the Treaty of Troyes and the birth of Henry VI.