I have some recurring calendar reminders set up that I really have no need or desire to see on the Start screen. Is there any way to selectively hide these from the Live tile, while still having them viewable within the app itself?
No. At the moment its not possible to select what to show or not to show, of upcoming meetings on the live tile. You can however, choose to turn it off.
On the live tile you can make a small tile so it wont show upcoming meetings, or you can go to settings, scroll all the way down and choose: Show on calender.
To hide from lockscreen go settings -> lockscreen -> and then choose what to show, or not show.