This is A M A Z I N G. Thank you so much for putting in the work of figuring this glitch out!

Which is amusing, because the only badges I have, I have because I started running this game, and grinding out the movement and the outdoors-time in story mode pushed me over the top for those badges!

I'd say no. Not everyone will have access to them (personally, I've only got two despite playing this game nigh-constantly before I picked it up for speedrunning, just because of the way I tend to play survival mode), and a couple would make a pretty big difference for speedrun purposes.

Can you even enable them in Story Mode anyway? I'd check but work.