my parents will rearrange the date to a day I can make it. However, it's not always a guarantee I'll feel up to it the new date either...

It's nice that they're so accommodating and want to see you but I get how frustrating that is because then there is never any "out" since it'll just be moved to a different date. :/ My family fortunately doesn't do that because the other people they want there have busy schedules so it wouldn't be feasible to rearrange for every single person, lol.

I need to find a way to say no, and to make them just exclude me from the large gatherings.

I've found that now that I've started saying no frequently enough I'm not asked about more random/non-occasion-specific gatherings as often. For the bigger ones they'll still ask me but by now they know there's a chance I'll say I can't make it.

I found saying no by email/text made it a lot easier at first. I also would sometimes temporarily put texts/emails from my parents on DND after so I wouldn't have to deal with a ton of back and forth about why I can't go or guilt-tripping because otherwise it'd be really easy to get caught up in a stressful back and forth with them.

I do know where you're coming from, I've been there too and still am sometimes. I used to wish I'd moved somewhere that was close enough that I visit and see my family often enough, but far enough that I had a built-in excuse not to be able to make it to events!