Now, I don't know much about your airplane, but if you can get ABOVE FL410, then you can legally transit RVSM airspace to get on top. I have done that in an airplane up to FL450. I would file to whatever your above FL410 altitude is and make sure that your ICAO filght plan has all the correct codes showing non-RVSM. Just keep saying that you are requesting transit of RVSM airspace.

I would not fly in RVSM airspace even if the controller allows it. You can still get a violation if a sup comes in or you get pushed into a different sector. Good luck.