I just want big cat eyes (i.e., lions, tigers, etc.) in a humanoid that can be just as expressive as a human's yet not having our very conspicuous eye-whites. Doable, yes or no?
Yes. Two ways.
For excellent simulation of this, watch one of the King Kong remakes. Kong does not have white sclera but they do a great job making his face expressive.
Or here are the chimps. You cannot see their sclera, usually, but they have very expressive faces.
The muscles of the face do a lot of the work too.
Alternatively, if you want a catlike pokerface but cooperative eye eye effect you could replicate the effect of white sclera by having very light irises and large pupils. Our primate cousins generally have very dark irises and it is hard to pick out the pupil and so hard to tell where they are looking. The majority of humans today still have very dark irises but because of white sclera you can tell where the iris/pupil unit is pointed - the cooperative eye effect. But you can have very light irises where it is easy to pick out the pupil in the center, and so see where an individual is looking. Some Europeans have light irises but cats do it best.