SpaceX has no warp-capable Enterprise class spaceship. He will probably give it a pass.
Yes, do SpaceX and actually go into space instead of the wimpy high-altitude flight. I'm sure he's got the money and it would be a better advertising. Can Captain Kirk handle a few days in weightless space?
And "training" for tourists should not be months. Might be fun but heck, they will be tourists, not crew!