In 5e, how can I offset the disadvantage created by not having a “big three” save proficiency?

I made a homebrew class. (I’m happy to share any details anyone deems necessary or even the entire class if it isn’t against the rules.) It’s a cha-based class which, for flavour reasons, has a variable secondary ability (depends on subclass). One subclass uses int, another uses str and the other uses wis.

It’s been brought to my attention that two of the subclasses suffer from not being proficient in any of the “big three” saves (dex, con, wis) while all 5e classes get one “big three” save and one of the other saves and therefore my class is at a disadvantage defence-wise 2/3 of the time.

The class gets a feature at 11th level that allows it to gain advantage on saving throws with one ability of its choice for a while, but it’s a once-per-short-rest thing and it doesn’t have access to that from 1st level to 10th level.

For flavour reasons, the secondary abilities and save proficiencies of my class’s subclasses absolutely cannot be changed; those two subclasses are stuck with not having any “big three” save proficiencies. How else could I offset the disadvantage this creates?

I’ve thought about bumping the save-advantage feature down from 11th level to 5th level and relying on low-CR monsters not having too many AOE/save attacks, but that seems like a really powerful feature for 5th level and I’m not entirely convinced by the idea.