You said a shoe with support, so you can probably disregard what I'm about to say since everyone's feet have different needs and you know best, but just in case it helps...
I've always had severe foot pain that gets progressively worse the longer I'm on my feet. My first DLR trip I honestly should have been in a wheelchair, but I was stubborn and since then I've learned better ways to cope. I used to look for shoes with support because that's what everyone says you should do, but I accidentally discovered that having adequate room for my forefoot and toes to move and having a heel that is not raised very far makes for lower impact and is way more important for preventing the pain than support. The best shoes I've found are definitely Altra, and the second would be Nike Free, but I don't think either would be described as highly supportive. Be warned that Altra's shoes are zero-drop (the heel is not any higher than the rest of the foot), which takes some people time to get used to, although I felt instant relief when I tried them. I still get pain but I can handle it without tears now. Last year I tried Asics because so many people recommend them, and just walking around my kitchen for ten minutes produced pain which I believe is due to the very raised/clunky heel which messed with the way I step. But obviously they work well for lots of people so it just goes to show there's no magic solution that works for everyone.
Also, equally as important as having a good pair of shoes is alternating shoes. If you have enough time before your trip, try to get two comfortable pairs of shoes and break them both in, and either alternate day to day or change shoes at lunchtime. It makes a surprisingly big difference.