Then you’d have to change your rule as written.
It could be as simple as "A pitcher inserted into the game after one or more at bats of an inning have already taken place must either
a) Complete the inning, or
b) Pitch to three batters.
A pitcher inserted mid-inning and removed prior to meeting either of these conditions shall not be permitted to play in his team’s two subsequent championship season games.*"
- = in the rulebook “Championship season game” is the term of art for a regular season game.
If you really must have a rule change like this, this is really all you need. Now you can’t have two switches in an inning unless the second pitcher pitches to three people.