Hi,
Based on your description I know what is the issue, but I cannot tell what can be the root cause. Best way how to find out will be to obtain verbose logs from Player and also verbose logs from playback in WPM Recorder, so we can see what is difference between Recorder playback and Player playback.
As to overloading is it possible that sometimes this peak happens due to longer playback times. Solution for this is obviously figure out what is root cause for longer transaction times or increasing playback capacity of worker.
Petr