I think ticking up is good for some things, especially for a slow burn. Like, we probably shouldn't count XP down from 355,000.

Sanity also works well ticking up, because you get things added to your character as you get higher (I am my normal character, PLUS a madness). An injury system that ticked up I would expect to come with penalties at certain points. Like, "At 30 wounds, roll on the Injury table and gain a level of exhaustion" or something. Most of this stuff works better if there's not a lot of variance between characters, too - 8 damage means something different to someone with 50 hp than it does to someone with 12.