Is this a correct formal heuristic for invalid moves due to Ko?
No, this logic unfortunately doesn't work: It prevents moves that are in fact legal, because they include a snapback.

$$ white to play
$$ . . . . . . .
$$ . . X O X . .
$$ . X O X . X .
$$ . X O O O X .
$$ . . X X X . .
$$ . . . . . . .


White captures:

$$W
$$ . . . . . . .
$$ . . X O X . .
$$ . X O a 1 X .
$$ . X O O O X .
$$ . . X X X . .
$$ . . . . . . .


Now with your definition:


  If in the previous half-turn exactly one single stone was captured


This is the case; white captured a single stone.


  then it is not allowed to play at the position of this stone in the immediately following half-turn (by the other player).


That position is marked as a. However, it's perfectly legal for black to play there, as it captures the whole white group, and thus does not repeat the board position:

$$W
$$ . . . . . . .
$$ . . X O X . .
$$ . X . 2 . X .
$$ . X . . . X .
$$ . . X X X . .
$$ . . . . . . .