Jon,
The only thing that would keep it from being able to be stabilized is dependent on the woods oil content. Woods like Cocobolo, Ebony, Wenge(I think), anyway you get the idea. If you look up a "Wood Encyclopedia", on line I'm sure you will find all that you need to know.
BTW, The woods that have a natural oil content to them, I treat as stabile, they will not absorb water, oil, or barely epoxy. In fact, when I expoxie Cocbolo, I clean the glued side with acetone AND alcohol, and once clean, immediately go to the epoxy process, in fear that the wood will "seep" more oil out to the outer edge that I just cleaned, now that is only my thinking, due to some I had come off using Acraglas, I cleaned them like any other, and went to do something else, when I got to it, I went on with the gluing process, now I know Acraglas will not let go willingly! I went through my procedure
(in my head) and the only thing I had done differently was the wait, while others where just clean and glue. I do not know if there is anything to back up my thoughts or experiences with or if I'm totally off my rocker, but every since then I clean it the way I mentioned I've have had zero failures! With stick tangs, I thought I was whipped with using Coccobolo or any of the denser Rosewood varieties, but what I came up with was to simply flush the cavity with acetone, let it sit for half a minute or less pour it out and then let it dry ( about a 1/2 min) then flood it with alcohol and let it dry, this time I gave it a good 5 minutes, then pour it out and give it a couple to 3 minutes to dry, before epoxy and so far! no failures. Also, the order should be acetone first, as acetone itself has some oil content to it, now I've not tested the theory that it HAS to be in this order, I just went with what I thought was right and got great results!
As far as the wood encyclopedia's go, if you've been on any of the big wood suppliers websites where they give you all the info about the wood, the growing climate, as well as where it's found, that's the kind of info you're looking for. It will tell you if it's an oily wood or not, you will always see this statement,"Polishes easily to a high shine". That alone is a sign that it has a high oil content.
Hope this helps, Rex