Recording and playing video with variable frame rate
Are you sure the files your recorded have indeed a variable framerate? It sounds like you recorded with a constant framerate (even though you get a variable frame rate video feed) which introduced this "artifact" and the players then of course play it back with a constant frame rate even though they shouldn't.

To properly convert variable frame rate footage into constant frame rate footage you can reside to Handbrake. It's an easy to use tool for h264 encoding that lets you choose to convert your video to a constant frame rate.