Hello Tmac,
I use one of these to unscrew those stubborn pocket watch cases. http://www.ebay.com/itm/New-Rubber-Vacuum-Pocket-Watch-Hand-Held-Case-Opener-/310544016336?pt=Pocket_Watches&hash=item484ddda3d0. It’s inexpensive but effective. Good luck 
I wish you well
Jim