If I may suggest:
I'm not convinced at all that graphite powder will make a contact. Conductivity needs so much graphite that the suspension is a paste, or even, it lacks liquid.
So before you invest time in mixing graphite in grease, oil, mixing oil with grease, and so on, I'd feel reasonable to mix graphite powder in any runny liquid and check at what consistency conductivity appears. If this fail, you won't have lost too much time.
To suspend much solid in a liquid, the general trick is to have several widely different grain sizes of the solid(s). Like concrete comprises stones, pebbles and sand. The smaller grains fill the voids between the bigger ones. With one grain size, less the 0.4 to 0.6 volume fraction of liquid makes a paste that doesn't flow. But if you mix three grain sizes differing by a factor of 10, the minimum volume fraction of the liquid drops to (0.4 to 0.6)3.
Whether this helps conductivity? I doubt it. Conductivity needs the grains to touch an other, and then the paste is immobile.
Did you consider completely different solutions? Like a spring that pushes the graphite brush against the platter? Or transmitting contactless with AC?
Generally speaking, this problem is difficult, solving it reliably is a matter of decade experience. Maybe a manufacturer of DC motors like Maxon would design a brush and ring for you.