I am also tied to a more linear visualization of timing things,so what works for most of the time is the trigger delay actor or comparator actors. also look at the media percent to time and timer actors to get time values.
I usually have the movie player play on it's own and use position output linked to a comparator if I need to trigger something along it's lenght,
counting pulses works but in my experience it is susceptible to time drifting due to load etc especially for longer lengths of time. Better use a timer to start with the first clip and then link an array of comparator actors to trigger other things as it counts towards your desired 20min lenght, then have it reset..