Another solution for making Str less likely for being dumped is adjusting the challenges the party runs into, favoring high Str/Int checks and saves.
High speed wagon chases where Athletics checks have to made to not fall off the sides.

History and religion checks when interacting with unusual foreign religions for not offending the powerful strangers you are negotiating with.

Those are what comes to mind off the top of my head. And to keep casters from dominating, if you are worried about that, remember: a) spells are resources, so if you use too many too soon, you wont have them later, b) except for sorcerors, spells are obvious when being cast and observors should react as such, especially in social situations, and c) anti-magic fields and chaos-magic fields are a thing.