I feel your pain. PF (and bad knees) ruined my trip to Paris, mainly because I didn't have the right orthotics yet. Physical Therapy and the right shoes have saved all my trips since then.
Ask for an extra ice bucket from the hotel. Put your ice packs or water bottle(s) in an ice bucket with as much ice as will fit. If there is room in the fridge, put the whole thing in the fridge while you sleep. When you wake up, the ice pack or bottle might be frozen, and you can bring it with you for some relief later. Put another one in before you leave for the day so you have something ready when you get back.
Ice in baggies works fine at first, but they leak when they melt, so you can't bring them with you.
If you have time before you leave, physical therapy exercises can help a lot. Stretching the calf, and using a balance board (which really works your foot muscles) helped me the most to get rid of the problem. Having the right shoes (broken in but not too much) and orthotics is essential.
I'm not used to walking long distances right now, so I have a lot of PT work to do before my trip to Disney.
Good luck!