Morgan's are game little horses, and a good one will do pretty much anything you ask of her. If she bores easily, I think Western Trail would be a great competition event for her. Every obstacle course has the potential to be filled with new things and some can be quite as challenging as eventing, if not as fast or high!
And just think of how much fun you could have in prepping her.... I'd love to ride a horse through a ravine filled with balloons!