you mean the BB cups & threads move around or the bearing races have lateral slack?

If the former, well I hate BB service and despise creaking, discovered quite by accident that the Loctite-like substance (thread locker? anti-seize?) that comes pre-coated on Race Face BB cups results in a no-creak, no-need-for-service-until-the-bearings-go-out BB installation so I have taken to cleaning oil & grease off of BB cups, frame threads and crank bolts and using blue Loctite with success so far. Zero creaking and I don't have to re-torque the BB shell, cup, and crank bolts every 1K miles like I do with Shimano BB's installed old school style with grease. I have been fighting this problem for a decade!

If the latter, the bearings are shot. They should not have any lateral play.

Either way I don't think grease is causing your drag... maybe bearing tension or wrong tolerance or something. The drag caused by the grease is so close to zero that there's no way you'd discover it by riding a bicycle.