I just properly installed BethINI today (thank you DoubleYouC for making this game program application tool, and thank you GamerPoets for the video on how to properly install it). I think there is a function in it to rectify this problem you're having.
EDIT: I checked a moment ago, it does, Always Run is on by default but can be turned off in BethINI. TESTED: I just turned it off, pressed File->Save in BethINI, closed BethINI, opened game in Mod Organizer 2, loaded my most recent save, and I am not running by default!
Get BethINI. https://www.nexusmods.com/skyrimspecialedition/mods/4875
GamerPoets' video about how to properly install and use BethINI: