I've taken freewheels apart and packed the bearings and pawls with grease. Tedious, but lasts much longer than oil. I used to read warnings that that would cause pawls to fail to grip in cold weather, when the grease becomes too thick. However, I've never experienced that hypothetical trouble, using synthetic bearing grease.
I do this with some higher end freehubs like DT. I do favor lighter greases, though. No issues with the DT Swiss grease and with Slick Honey. Never tried NLGI 2.