Well, I finally found my solution. OP, I don't know if you have already gone on your trip or not, but if not, maybe this will help you. I ordered a Baggallini Bryant Pouch. It is AMAZING! It is only 6.5” tall, 4.75” wide, and 1.25” deep. Even though it is tiny, it holds a lot! I have been able to fit my phone, my lip gloss, hand sanitizer wipes, floss, a poncho, mints, a pill box, a key, my driver's license, my health insurance card, a Disney GC, my DVC card, a Landry's card, and there's still some room left over! It works as a crossbody, a wristlet, or a fanny pack. I bought it thinking I would use it as a crossbody, but I think I like it as a fanny pack better. It's very light even with all those things in it since it weighs only 5 ounces empty. I am going to try to avoid bag check by sticking it in my back pocket with my phone in the other pocket. Then as soon as I enter the park, I will clip the Baggallini onto my hip and stick my phone in the front pouch. Totally hands-free! (I ordered it through Baggallini on sale and with an additional 20% off, but it's also available from Amazon.) https://www.amazon.com/dp/B015GJ1XIW/ref=twister_B07MW1BV94?_encoding=UTF8&th=1
Update: I traveled with my Baggallini last month. I used it as a fanny pack most of the time which was wonderful! I went through bag check a few times since there were others in my group with bags. A few times I went through the no-bag line with no problems. Two times (one time with my DH and one time with me) we were asked to take it out of our pockets. I forgot what they asked my DH, but they asked me what it was. I said a wallet. I had to open it there but was not sent back through bag check. The reason I was asked to remove it was because I had it filled with everything except my phone, but it was still noticeable in my pocket. Next time, I'll probably divide all its contents into our pockets and leave it completely empty so it's less bulky. Then when inside I'll put everything in.
ETA: My DH did not have to open it when he had to take it out of his pocket.