Shimano's Nexus grease is quite thick--an NLGI 2, for sure...but it has a neat trick: it's soluble in their lubricating oil for Nexus hubs. If you have any chemist acquaintances, they may be able to tell you what the base of both are, allowing you to thin them without destroying the lubricant.
I will say that the standard service procedure is simply removing the internals (unscrew the left side, not the right!), dipping it into a vessel filled with heavier oil, then pulling it out to drain back in for a minute or so. Afterwards, put grease on the planetary cogs through the gaps, the roller clutches (if present), and reassemble, applying grease to the LH wheel bearing before closing it up.
You need a couple of tools to remove/install the RH cone to get access to the other wheel bearing, which is a weak point in the service. It otherwise never gets greased, and will eventually fail entirely...necessitating the replacement of the driver assembly, since it houses the bearing race.
