Hello there,
I'm a European/UK R&D engineer from a very highly prestigious consumer electronics and MS WIndows/embedded background, and come with vast C++ experience, and some QT too. I only though, offer Windows and Linux based services; not Mac OS.
As for FFMPEG, it uses DirectX on WIndows, and I have used and developed raw DirectX filters for a long time now; especially for camera streaming, audio conversions; and desktop recording too.
And with DirectX, you can add pauses to a video stream, since each stream is a "stream/sequence" of H264/JPEG frames - that then get merged to form a video; so it is possible to add a pause option, in between incoming streams; as long as one has access to the QT/FFMPEG code; if not, it would be visually impossible to externally pause a video stream - unless, alternatively.... one pauses the THREADs that is streaming the video/audios, using Win32 functions PauseThread() and ResumeThread(), from an external C++ program that I can develop for you. Whether this will work to achieve your goal, is not guaranteed, as I've not tried it before.
if interested, I would first like to have a demo of this software, working, and take a look at it's "thread pool" using a one of the process monitoring tools that are freely available on the internet.
More later, if I hear from you..
Cheers
Dinesh