qaws-
As hello99 said, the gemara says hard cheese is a problem. In fact, my rav holds that although c.s. is mutar lechatchila for everyone he still holds that hard cheese is assur, because there is a gezeirah in the gemara against gevinas akum regardless of how sure we are that nothing was added – it is similar the gezeirah of pas akum and bishul akum.
Powdered milk has another heter besides what you mentioned. R’ Ruderman and R’ Tzvi Pesach Frank held that since powdered milk did not exist at the time of the gezeirah (assuming there was a gezeirah on milk and not just cheese, not like my rav) it never became assur.