I haven't been here for a while and didn't see your answer. Thanks for chiming in Danny!
I did what you suggest - hided all PT windows, but nothing, really nothing can't stop the stutter (except the OS restart, that sometimes solves the problem for a few minutes or so).
As you noticed BlackMagic should have solved that, but it didn't. I suppose, that in my case the computer itself is the problem. Therefore I'm going to replace my Mac, which is old guy anyway, with newer machine. Hope this will solve the trouble permanently