You are basically right. That's what makes the job of the federal reserve bank so hard. They need to measure V and T, which you rightly point out is not easy, and then they need to adjust M to keep P stable. And as you further rightly point out they only control a small part of M, i.e. the amount of cash. It basically works by the Reserve Bank having a good guess at V and T and then adjusting the cash rate hoping that it will encourage banks to adjust their general loan rates accordingly and thus having a significant enough impact on M.