Finally got it figured out and decided to post what I found incase anyone in the future runs into the same problem!
So, originally I was using my brothers copy of Pearl and could only access 19 of the trapped Pokemon- even after following the instructions to the letter. After finally managed to get a copy of Diamond to mess with and doing everything again, it worked! I was able to get all the other Pokemon out safely!
I don’t know what’s going on with the code behind it all- but I assume there’s something in the background of Ranch that logs not just what trainer added what Pokemon, but also what version was used to send them over.
So for anyone else that runs into this problem, if you shared the file with siblings or friends with different versions, you might need a copy of both Diamond and Pearl to get everything out of your Ranch!