In a related question, do you have any ideas for topics of interest to e.g. transhumanists, which could be suited for a Master's or PhD thesis in physics, and for which finding a supervisor does not sound straight out impossible?

Well, various incarnations of Many Worlds/Mathematical Universe/String theory landscapes/Boltzmann brains are popular both here and in many Physics circles. While I don't hold much stock in any of those, there are surely some tenure profs in physics departments around the world who would take a sucker grad student willing to spend 4-6 years on something like that.