1. Ra8+ Ke7

2.Qxh8 Qxh8

3. Rxh8

still come out the same way

Why not Ra8+ first? then Ke7. Rxf8...Kxf8. Qxh8+

Because of 1. Ra8+ Ke7 2. Rxf8 Rxf8

1. Qf6+ Qe? 2. Ra8#

1...      Kc8 2. Ra8+ 2. Kb7 Rxe8 and white is a queen for a rook ahead rather than just a rook. Of course white already has a won game with 3 extra pawns. However I take the point of the x-ray attack regaining the queen.

 Ur first alternative isn't a forced mate cause of ur second, a queen for a rook and a queen is a better change then rook for queen, especially when as u say white has 3 more pawns...

 I see ur point, I didn't see it when I made the puzzle...

I think I prefer the text moves as it's the only way to guarantee both of Black's remaining major peices come off the board.  Pawns aside, I'd much prefer K+R vs K to K+Q vs K+R.  Even McLovin369's vairation allows Black to escape with K+Q+R vs K+Q if he so desires.  The text is decisive.  Good puzzle.