Mobilgrease 28. It's pretty much the industry standard all-purpose grease. Some OEMs specify it.
My personal opinion is that the conductive/non-conductive argument is a complete non-issue. Mobil 28 is actually a mechanical grease that I believe was designed for use in the aircraft industry, yet it still gets recommended by OEMs for contacts and stabs.
We routinely put it directly between flat mating surfaces and still have great low-resistance connections: I think as long as excess grease is allowed a path to escape so you're not building a hydraulic seal, it makes absolutely no difference because the grease itself is not a current carrying component. My guess is the high-points on the mating surfaces cut through the grease as long as it is fresh and pliable.
I would actually be very wary of using anything with solid metal "conductive" filler because it seems to me those could create a physical barrier between connections: It's anecdotal, but I've seen several destroyed groups of breaker fingers where somebody used copper anti-seize, probably thinking it would improve the connection. It didn't.
Use something that isn't super viscous but still won't drip everywhere at high temperature, and make sure you don't mix different lubricants. Other than that, I think it's pretty immaterial.