Here is what I get searching the go4go database with kombilo:
#1) Instead of extending at B6 (move

) The most common play is to connect:
- Click Here To Show Diagram Code
[go]$$Wcm1
$$ | . . . . . . . . . . .
$$ | . . . , . . . . . , .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . 1 . . . . . . . .
$$ | . X O . . . . . . . .
$$ | . X X O O O X 4 . , .
$$ | . X O X X X O X . . .
$$ | . O O 2 . X O 3 . . .
$$ | . . . . . . . . . . .
$$ +----------------------[/go]
149 pros played your way vs 254 that connected as above -- not quite twice as frequent.
The continuation is as follows:
- Click Here To Show Diagram Code
[go]$$Wcm1
$$ | . . . . . . . . . . .
$$ | . . . , . . . . . , .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . 3 O . . . . . . . .
$$ | . X O . . . . . . . .
$$ | . X X O O O X X . , .
$$ | 5 X O X X X O X . . .
$$ | . O O X . X O O 4 . .
$$ | . . . 1 2 . . . . . .
$$ +----------------------[/go]
And then black tennukis. I don't know if you find this trade better, but it's at least an alternative, and maybe since more pros play this way it's worth considering?
Given that you extend as you did in the game, connecting is still the most common response after white plays atari (110 plays vs 39):
- Click Here To Show Diagram Code
[go]$$Wcm1
$$ | . . . . . . . . . . .
$$ | . . . , . . . . . , .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . 2 1 . . . . . . . .
$$ | . X O . . . . . . . .
$$ | . X X O O O X 6 . , .
$$ | . X O X X X O X 5 . .
$$ | . O O 4 . X O 3 . . .
$$ | . . . . . . . . . . .
$$ +----------------------[/go]
Then either white jumps and the fight continues like this, with white either a or b next:
- Click Here To Show Diagram Code
[go]$$Wcm1
$$ | . . . . . . . . . . .
$$ | . . . , . . . . . , .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . X O . 1 . . . . . .
$$ | . X O . . . . . . . .
$$ | . X X O O O X X 2 4 b
$$ | . X O X X X O X O 3 .
$$ | . O O X . X O O . . .
$$ | . . . . a . . . . . .
$$ +----------------------[/go]
Or white pushes and something like this happens:
- Click Here To Show Diagram Code
[go]$$Wcm1
$$ | . . . . . . . . . . .
$$ | . . . , . . . . . , .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . 6 . . . . . . . .
$$ | . X O 7 3 . . . . . .
$$ | . X O 5 4 2 . 8 . . .
$$ | . X X O O O X X 1 . .
$$ | . X O X X X O X O . .
$$ | . O O X . X O O . . .
$$ | . . . . . . . . . . .
$$ +----------------------[/go]
So again I don't really feel qualified to say this result is better for black, but it's a more common way it seems.
Finally, white's push

at a doesn't occur at all in pro play, the common responses are either attach at b or jump to c:
- Click Here To Show Diagram Code
[go]$$Wcm1
$$ | . . . . . . . . . . .
$$ | . . . , . . . . . , .
$$ | . . . c . . . . . . .
$$ | . . X a . . . . . . .
$$ | . . X O . . . . . . .
$$ | . X O . O . b . . . .
$$ | . X O . . . X . . . .
$$ | . X X O O O X . . , .
$$ | . X O X X X O X O . .
$$ | . O O X . X O O . . .
$$ | . . . . . . . . . . .
$$ +----------------------[/go]
The closest I could find were two games where white attaches first and then pushes. Black plays hane at a as Joaz suggested, or turns with the cutting stones at b:
- Click Here To Show Diagram Code
[go]$$Wcm1
$$ | . . . . . . . . . . .
$$ | . . . , . . . . . , .
$$ | . . . a . . . . . . .
$$ | . . X 3 . . . . . . .
$$ | . . X O . . . . . . .
$$ | . X O . O . 1 b . . .
$$ | . X O . . . X 2 . . .
$$ | . X X O O O X . . , .
$$ | . X O X X X O X O . .
$$ | . O O X . X O O . . .
$$ | . . . . . . . . . . .
$$ +----------------------[/go]
Given that pros don't play that push, it's tempting to see it as a bad move (it is pushing from behind), and I wonder if black could get away with something like this:
- Click Here To Show Diagram Code
[go]$$Wcm1
$$ | . . . . . . . . . . .
$$ | . . . , . . . . . , .
$$ | . . . . . . . . . . .
$$ | . . X 1 . . . . . . .
$$ | . . X O . . 2 . . . .
$$ | . X O . O . . . . . .
$$ | . X O . . . X . . . .
$$ | . X X O O O X . . , .
$$ | . X O X X X O X O . .
$$ | . O O X . X O O . . .
$$ | . . . . . . . . . . .
$$ +----------------------[/go]
But like I said, I don't actually know anything about go, only about querying databases
