the shelf life of grease in a closed package is probably a century or so. Most grease goes bad, not because of any chemical problem, but because open containers get contaminated with all kinds of stuff.

Visit any bike shop and you'll find an open tub, collecting dust, and whatever is introduced by the brush which is used to apply it, and return dirt back to the mother ship. The smart way to buy grease is in tubes, or if in tubs, to transfer a small amount to a piece of scrap paper or foil, use what you need, and discard the rest. Otherwise all your effort to repack bearings in clean room conditions will be for naught.