Issues with my strumming hand position playing a Strat when sitting

Yes…especially barre chords, IME.

I play a Les Paul style guitar and have the same issue sitting down - as I have shoulder problems, it can really be a problem.
Something I want to do in the future is get a jaguar/Jazzmaster style guitar for seated playing - the waist on them is set further back, so the natural arc of the arm should take the fingers over the pickups rather than the neck (it is way more comfortable for my shoulder when I play over the neck or right near it at present)