I thought the issue might be that the character is a max level barbarian and the 20th level ability sets the max CON and STR to 24, but I leveled the character down to 19 and the ability scores just cap out at 20. 

Is what I have (I understand the number is absurd but this isn't for a campaign or anything). 30 doesn't work either, not sure where I'm going wrong.

Looks like the max score is 30, no matter what you do

Please see the Homebrew Subclasses & Species FAQ #12: (https://www.dndbeyond.com/forums/dungeons-dragons-discussion/homebrew-house-rules/131411-a-homebrewers-how-to-faq). And yes, the maximum is 30.

The stacking bonus just sets the ability score to 30, but I just want the cap to be 30, which the ability score maximum on it's own doesn't do for some reason.

The Ability Score Maximum does set the max at 30, but without the Stacking Bonus, it he score still won’t go above 20. The Maximum makes it possible, the Stacking Bonus makes it happen. If your character has enough regular bonuses to add up to 30 it still won’t actually go past 20, you need Stacking Bonuses to actually go above 20.

That sucks, but then how does the 20th level barbarian skill work? If the regular bonuses aren't counted as stacking bonuses, but can still go over 20 in that instance, the 20th level barbarian skill must have some kind of special property no? 

The 20th level barbarian feature includes a Stacking Bonus of +4.

If you have a PC with a stat at 18, and you raise the Max to 30 and add a Stacking Bonus of +4, then the PC’s stat will go to 22. If that PC’s stat was 20, and you raise the Max to 30, and give it a Stacking Bonus of +4, the stat will go to 24. What part of it doesn’t make sense? Lemme know and maybe I can explain it better.

No no, it makes sense, the barbarian feature adding a +4 stacking bonus explains it, thank you 🙏

Happy to help.