In my experience with grease and fast spinning gears, the grease gets "slung" off the gears pretty easy and sticks to the sides of the case while the gears tend to run dry. I would use like a "Lucas Oil Stabilizer" or a "Power Punch Oil Supplement" in there I think. It is thick and super slick. Just pull the plug and squirt some of this up in there.
You can get the "T" fittings at any auto parts store. You could use brass or plastic because there is no pressure on these lines.
Aaron
Keep in mind though, that the presence of at least SOME premix in that center section is inevitable, which would thin the grease out significantly. Either way there would be a small amount if time where it would act the way you just described before the premix has time to seep in there in a quantity significant enough to thin the grease.
I may add a more middle of the road lubricant next time, but my thought was that the thicker grease would stick around longer.
Btw, the issue of running the sled lean with premix has been brought up a couple times, I ran one 07 lean enough to burn down 5 times while running premix. It never had a problem with the delete in all that time of being on the ragged edge. I can see it being a factor, but I think I subscribe to what bgreen said at one point, some sleds just allow more oil to seep through than others. Obviously I have had ones that allow more rather than less.