What are the FAA regulations on operating UAVs in class E airspace above FL600? What are the regulations on flying UAVs (commercial or experimental) above FL600, i.e. in class E airspace above class A? I want to make a HAPS (High Altitude Pseudo Satellite) and operate it in the higher altitudes.

Is there a way to do this without a pilot's license (I don't know if I can pass TSA background checks)? How high do I have to fly to be above class A and in the class E airspace? Would you recommend launching from international waters? And how high should I fly to be in space or in completely unregulated and uncontrolled airspace?
The FAA limits drone operations to 400 Ft. so getting to FL600 is not really possible. 


  Cannot be flown higher than 400 feet above ground level (AGL), unless
  flown within a 400-foot radius of a structure and does not fly higher
  than 400 feet above the structure’s immediate uppermost limit;


The FAA does offer a waiver process for flying drones beyond the regular part 107 rules. You can find all the info on that here. The request to operate in controlled airspace form does ask for a max altitude so its possible it can be requested. 



However someone in Russia appears to have flown their drone up to FL330 so it may be allowed there.