Hi Garrett - not sure how you'll be carrying your bottle for EDC? I have on in a bottle pouch, which keeps the cup with it without a problem. Sounds like you're planning to carry it with the bottle exposed. I keep a bandana in the bottom of the cup, with one corner of it peeking up past the lip of the cup. It keeps an extra bandana handy, and the cup is snug enough to the bottle that that little extra material wedged in there makes the cup stay on pretty firmly. However, if you're carrying it, for example, with the cap's loop around a belt and the bottle swinging free, I couldn't recommend the bandana as a secure solution.
Hope that helps
Dave