I have rheumatoid arthritis so I have joint pain all the time - specifically worse in my wrists, hands, feet and ankles. Although my flare ups hurt my neck and jaw.
I find sitting with ECVs worsens the stiffness but allows me last longer in the parks as fatigue is another RA issue. I am trying to improve my endurance so have switched to a rollator for going out (but not at theme parks yet).
the walking isn't so much my issue, it's the standing. The standing hurst my back, hips, ankles and feet. You may find a rollator can help with that if you don't want to use an ECV. It will allow you to sit when you need and a support when you're walking.
ECVs can run out at the parks. I'm not sure how immediate availability is with private companies but you could rent it as an insurance plan. I have seen that places like Golds Mobility will sell out for certain times of the year. If you're onsite, you could rent the ECV, ride it to the parks and then leave it parked near the front and then walk around and then take it back. I'm all about making my day easier so when I go again, I'll likely rent the ECV (maybe not for the whole trip) and have it as back up.