tl;dr: As long as you have enough available credit, if the "balance transfer" will pay you cash directly into a bank account, then you can do what you propose.
...I heard that, due to the CARD act, only the minimum payment may go
toward the lowest APR, and that any additional payment must go toward
the highest APR
That's correct. Prior to the Credit CARD Act in 2010, banks could apply extra principal however they wished, and typically they would apply it to the lowest interest first because it was more profitable for them to do so. Beginning in 2010 in the US, all consumer (personal) credit cards must apply additional principal payments to the highest interest first. The fact that the lower interest rate is a promotional rate isn't relevant. This is a good thing for consumers.
Nowadays, likely because of the CARD Act, most banks won't let you take cash for 0% to prevent what you propose; instead they force you to pay off some balance from another bank. However, if they do give you cash, I don't think they could stop you from replacing your 12% with 0%. Note you typically will have a fee of 2-5% up front as well.
Tip: If you succeed in converting the high interest to lower, consider dividing it up into equal payments so that it is fully paid off by the time the promo rate expires.
Note that the law does not apply to business credit cards; only consumer cards.