You really don't want to answer the question!
The Pilgrims did not have the ability to pitch a rock from the new world and destroy London. Your like-minded people will. So I think that the trust and good will of the people in London may be critical to your scheme, where it was not back in the 1500s.
Your "...who cares what those back on Earth think?" suggests that you would not be one of those who would be trusted. I would not want you and your like-minded people up there, nursing grudges, and wondering what to do with the mass drivers, ion engines, and nuclear reactors you were building.