You're not crazy, vibes and competitor prices is how many, many shops roll. (I really like "vibes and competitor prices" a lot, may have to steal that!)
The good news is that for your basic 16oz iced latte, you're at 20.6% COGS, that's GREAT for never having run the menu-item level COGS before! Many find 40+%, so you're starting from a great spot on that one!
I also love that you're seeing "there goes a quarter, there goes a quarter" now, too - the next step with that is finding ways to either keep them from using the to go cups (we bought cheap tumblers for the staff to use at work, gave them fun coffee stickers to put on them, and that worked - just have to keep reminding them to use them on shift). Finding new places for less expensive cups, lids, stickers, etc is absolutely the right next step.
Have you looked into stamps at all? I've heard some owners say they really like the look, though I'm not sure how well they stamp the PET cups for iced drinks. Maybe those have to be stamped earlier so they can dry before filling?