I know this thread is ancient, and I'm new here, however, through some HEAVY googling, too much YouTube, and a few weekends if trial and error, with the grease/oil based bar drying out, I have a working solution! (I created an account here SPECIFICALLY to share this knowledge, and after poking around, I'm happy I did as the wealth and breadth of knowledge here is remarkable!)
If you know your going to store your green bricks, apply a thin even coat of quality olive oil, then I plastic wrapped and ziplock bagged the bar.
5 years and 3 months later, although a noticable shade darker, it function s as if just off the assembly line!!

(This experiment was actually done under my father's advice, stored, and completely forgotten about for many years, till hours before writing this message!!
*Of all the things I have lost,
I miss my mind the most!* Right??)
NOW,
If already dried and performing akin to chalk, a similar method is employed, with a few repeats on a couple steps.
Simply apply a good even coat of quality olive oil to the exterior, ziplock it with as much air removed as humanly possible, leaving it in a warmer place, like cupboard above your kitchen stove, for a day or 3, untill the surface is no longer shiney.
Rinse and repeat once or 2x more.
After a couple weeks, I broke one of the bars in half, and all but a 1/2 of the very core was "rehydrated" (for lack of a better term), and functioning as expected!
*** No need for 4 or more coats, unless your after a green bar paste!! (Yes, I found out the hard way - now relegated to the Dremel buff & polish tool box! -that amount will last DECADES! Hahahaha)
SO,
If you need it immediately, although I've not tried, this method, but stands to reason - apply a light coat of the same quality olive oil to your buff to load it strap, them apply green, but slower strokes, to kind of allow some level of surface absorption.
I tried to figure out a process to revive these great, multi purpose, green bars of wonder (seriously, look it up! These are the duct tape of polish compounds, with dozens of off lable uses I found on instructables & reddit!), as I acquired 11 bars dirt cheap, from a business that went under due to Covid a year ago.
However upon closer inspection when I got home realized they had been manufactured at least 5 years earlier and several had the packaging cracked in one or 2 corners, & had obviously been exposed to the elements for years. Even the ones that were still in their sealed blister packages seem to be suffering from some sort of drying
I didn't have the heart to throw 30 something pounds of green bars into the garbage being the upcycler at heart I am lol!
I truly hope this helps someone get years more shelf life - decades even, I would assume!
Stay safe all!!