My son has worn Alcon Dailies toric lenses for ~6 years, and has never had any issues. Daily lenses are the way to go--the plastic waste from the packaging is kind of a shame, but no concerns about getting a teenage boy to properly clean and care for them. And keeping an extra pair around is dead easy. Keep a small bottle of saline drops in your baseball bag, too. My son played a game 2 weeks ago in high winds--his lenses were drying out pretty badly on the field.
As you probably already know, toric lenses are a good deal more expensive. But as for the kinds of problems you mention about vision changes due to the lenses moving? Never been an issue, and never mentioned by my son's eye doc. (And fwiw, he is a PO now, but wore the lenses for several years when he was also a position player/hitter.)