One of a number of reasons I hate castling in Chess 960
The Orthodox Rule is the one you learned in your chess rules that came in your first box. Move your King two spaces toward the Rook, the Rook jumps to the space your King moved over.
Guess that is too complicated if you can't even get it right in the example above. 
(0-0-0 Rook lands on B1.)
The King landing one square from the edge of the board (B & G) changes the game from the FIDE rules for the original opening positions. This would be really confusing for FIDE Chess players who started from that position. Other than that, it's a good idea.
- The King moves first, because that's how it's done in FIDE Chess.
- The King moves two squares because that's how it's done in FIDE Chess. (Exception is made for the corners... this is the only major flaw I see in "Orthodox Castling")
- The mirror image of the standard FIDE Chess starting position is particularly hard to understand in Chess960 because of the oddity of the landing squares for opening (book) theory.
That said, again, your suggestion of moving to the second square is intriguing, but how do you deal with starting positions where the King is already there? In Chess480, the King always moves! It's a mantra I want to emphasize. Castling started as a King's Jump of two spaces. That's why the 0-0-0 move (in FIDE Chess) doesn't get you closer to the corner.
As before, I'll repeat that I like your idea of moving to the B and G spaces (with the Rook ending up on C and F respectively.) It has merit except for the issue of the one starting position where it will cause problems.
[The moving into the space with the Rook, should it be two spaces away, if very similar to how one captures a piece and should feel natural to players, so I'm not going to address the issue of moving "onto" the Rook.]
As I said before, I like you idea. (BTW, you should give it a name.)
It fails the idea of expanding FIDE Chess because you can't play the classical version of the game. This was a key aspect of Fischer's vision and the impetus for trying to improve on the Chess960 castling rules.
There's a lot I would "fix" about Chess if it were a new game, being developed. I don't think I would allow castling at all, but instead re-insert the King's Leap if shuffling of the back rank pieces were the desired feature.
That said, we aren't there and there's only a few thousand people in the world who even care enough to be interested. We aren't changing the world here... just talking about something we both obviously love.
Cheers.
https://www.chess.com/blog/ArnieChipmunk/kasparov-the-king-s-gambit-and-opening-theory-before-castling
And interesting article on castling here.
From this position there are two options for castling. In 0-0-0, or "Queenside" castling, the King literally doesn't move and the Rook jumps over the King like a leaping piece. In 0-0 or "Kingside" castling, the King moves four spaces and Rook doesn't move at all.
One of the many reasons I prefer "Orthodox Castling".