I've been training my STR stat with the gym minigame and I've noticed an unexpected but very beneficial exploit. Training STR has had the expected result of also increasing CON (and therefore Health Points), but I've also noticed my character's Mental Points improving as well. This is a very nice perk, raising resistance to Anger, Depression, Apathetic status ailments. I'll certainly be taking full advantage of this silent XP bonus. Hopefully the devs don't get wise and patch this it out.

Side note: I've heard that overtraining STR can lead to the Body Dysmorphia, Injury, and PED status ailments, so be sure not to forget about the main game while trying out new minigames either. Ideally, make sure to do your first few runs with someone who is a higher STR level than you and knows the minigame well so that they can guide you on how to maximize your XP gains and minimize your risk of the Injury status ailment.