You should have put a link to this discussion that says that copying a movement type could solve your issue. I actually think you found a discussion with a wrong answer.
If you do not want that the prices flow, then you have to goods issue (e.g. 201 movement) your new tires and reverse goods issue (202) at the old tires. The difference value remains as cost at the cost center.
You can alternative use 309, and subsequently change the new moving average back to the old moving average using MR21 transaction. This creates a price change document and stock adjustment posting in Finance.