Small Drywall Tiles for Ceiling
All you accomplish by hanging small pieces and then taping all those joints is to add more fasteners and more lumps in your ceiling. The taped joints effectively make it all a single sheet, just as it would be if you hung larger sheets. 

Do a little math and you'll realize that each fastener already only holds up a small bit of drywall, on average. Adding joints actually makes it all less stable.

Deal with your irrational fear and do it the right way. Add more fasteners if it lets you sleep at night, but I can't imagine that this is the only thing preventing that.