I think your biggest problem is that there just weren't enough nativese relative to the white population coming over. There was something like two million inhabitants north of the Rio Grande at the time of Columbian contact, relative to about 50 million south. Thus, even if you do get the breeding of the two peoples, you just end up with white people who have one great, great grandfather being Cherokee or whatever, rather than mestizos as such.
Your best chance is to get the British take the Yucatan, or another place with a dense native American population, and then use the "wildness" of the place to put off white women coming over.