You got everything right, but in my experience TurboTax handles the AMT credit just fine. I personally recouped 6 figures of credit carried over across multiple years, and TurboTax always automatically calculated the usable credit every year, and when I ultimately sold the exercised shares it also properly computed the different AMT cost basis, allowing me to recoup even more that year due to the higher spread.

I would still recommend folks to properly understand what it is and how it is calculated so they can double check the numbers, but that really applies to pretty much every tax form.