I just posted a solution on a totally different question, where the approach I used might work well for you here also. That user also wanted to filter at the month level. I used two disconnected date tables to define a start and end month, and then harvesting those dates created a 0/1 dummy variable measure reflecting the logic of the records he wanted to show, and then put that measure in the filter pane and set it equal to 1. I think that approach would work well here, defining the dummy variable both in terms of the start and end dates, but also the minimum minute threshold.
See what you think. I hope this is helpful.
– Brian