Let me explain.

You said:

> Flip it twice. Once to determine which side is up at second throw. Reverse to counter bias at start of second throw. Then flip again for final result.

Suppose I'm throwing the coin using your technique and I want to favor heads.

I hold tails up for the first throw, making tails more likely.

Then as per your rule, I put heads up for the second throw. Now, heads is more likely.

Choose the opposite starting face to make tails more likely. So, your technique does no prevent the coin tosser from being able to favor their desired outcome.