To make the sentences synonymous, it would be better to place "still" right after the subject (before the modal): "Our team still might win" <--> "Our team might win yet"; "I still might beat this cancer" <--> "I might beat this cancer yet."
With "still" placed where you have it, after the modal but before the verb ("Our team might still win"; "I might still beat this cancer"), it is as if there were an implicit "in spite of" or "regardless of" or "even with," etc.
- Our team might still win, no matter what they say.
- I might still beat this cancer. Doctors have been wrong before.