You rang? I have expertise in both FRCFIRST Robotics Competition grease and non-Newtonian fluids!
(Bad dispensing aside, we see similar behavior in our wheels/gears.)
Grease is most often non-Newtonian in my experience. This means that its viscosity changes with stress, and most greases are thixotropic. But what does that mean? It means the grease gets thinner as it is sheared/squeezed/flows, and more viscid when it isn’t being deformed.
How does this explain what you see?
When the gear compresses the grease the grease is both displaced/pumped and made less viscous. Half-ish goes outwards and is slung away. Half-ish goes inwards, stops being deformed, and becomes firmer again. This grease can just kinda hang out on the inside lip of the bevel gear between its higher viscosity and lower acceleration. We will just wipe it away when it builds up.
Mobil XHP 222 is the recommendation since EP1 is out of stock at McMaster.
Also strongly recommend syringes and needles for application.
External grease should be attended to regularly. Minimum once per day if the robot is driven at all. I ask my students to regrease every 2-4 battery’s worth of driving. You don’t need a ton because excess grease is pumped away almost immediately, a little dab’ll do ya.
For engine and transmission assembly, absolutely. For FRCFIRST Robotics Competition robots it is wildly too expensive and not particularly appropriate.
Assembly lube is designed to work for initial startup only, then get dissolved into the engine/transmission/differential oil and flushed out after break in. It isn’t intended for more than momentary usage. XHP 222/EP2 is specifically designed for open gear lubrication and won’t get slung off quite so bad as assembly lube.
A real grease for open gears, like XHP 222/EP2, costs $5-6/14oz instead of $11/4oz of Redline assembly lube. The redline is thus 6x more expensive.