I have had very iffy results with setOptions on the scheduler... some things work, like toggling work hours, many things didn't, like setting selectability. I had to destroy and re-create my scheduler to set certain options when they changed.
You may have to destroy the scheduler (Here is documentation on this) and recreate with your new min and max.
Another approach that does not involve destroying and recreating your scheduler, is in the navigate event, check the date you are navigating to, if it exceeds the bounds of your min and max, e.preventDefault() to stop your scheduler from doing anything or scheduler.date(previousDate) to return to the date range the user was just on and pop up a warning or something saying that is as far as the scheduler goes.
But I believe your issue is the destroying and recreating. To utilize the min and max date, you most likely will need to destroy and recreate with those options set. To avoid that, you can utilize my suggestion to catch and stop the user going beyond the min and max date in the navigate event of the scheduler.