I used to use a Production Press tool white grease (possibly Castrol)that contained a large proportion of molybdenum disulphide content for tooling that was inaccessible or critical to production,donated by the teaspoon from work.
Now for my next lube session I will buy a nz$70 tube 60% moly off our local BMW guys that specially import it ('cause Castrol doesn't).
Most greases will contain around 3% moly.Not Nearly enough for our application where high local temps and pressures and,effectively,neglect are experienced.
Guard dog have 30% moly.
The moly sticks to the metal long after the carrier has dried out so "flick off" might not be too concerning?