My preference is to not grease cables. Grease just invites dirt to stick to it, so ultimately it creates a bigger problem.

Assuming it is a cable friction problem, consider these things:

-use good stainless, extruded (pre-stretched) cables, they are smoother than the cheapest variety.
-use good housing with a lining.
-Are any of the runs too long? Even in the best of circumstances, cables rub on housing. Minimizing the length minimizes the friction.
-Are any of the runs too short?

Each of these factors are probably very small. But, it is always surprising how small the friction variable needs to be to impact shifting.

Also, from how you describe it, it sounds like it could possibly be a sticky shifter itself.

jim