It turned out to be nothing more than a filesize issue. Every time I would save the PACs, the sizes would inflate. With a little trial and error, shuffling among PSA versions 1.3, 1.9, and 2.35, I eventually got the filesizes perfect and they work perfectly in my Brawl now, no freezes.
For me, PSA version 1.3 worked for Dedede and Ivysaur, 1.9 worked for Squirtle, and 2.35 worked for Charizard. When I say "worked," I mean it saved them at the correct filesize and didn't inflate. I'm sure it was completely random that I got the filesizes correctly saved, so I don't think it'll work the same way for everybody, but that's how I solved it.