I continue to have success with this relatively simple method:
Wrap the bottle and stopper in a paper towel, and go sit down someplace comfortable. This will take awhile. Grasp the stopper in one hand and the bottle in the other and then very firmly "bend and hold" first one way, then the other. Again and again, in all directions. Do not twist, do not pull, do not use tools. Just bend and hold.
This bend and hold method allows the glass to flex slightly, which allows air into the bottle in microscopic quantities, while it encourages the liquid perfume to slowly migrate into the ground glass seal, which then softens any hardened reside and allows further movement. You may be causing the most imperceptible movement by this repeated bending, but it works.
The reason, I believe, is that over a period of time a vacuum actually devlops inside the sealed bottle. The alcohol and some perfume oils go out, but not much air actually goes in. So part of the reason that getting the stopper out is so difficult is because it is actually under vacuum pressure. (Hmm... if is was under positive pressure, getting the stopper out would be pretty easy).
I have tried a variety of hot, cold, soaking, tapping methods but this bend and hold method always seems to work. Work at it for awhile, then give it a rest. Then come back and do it some more. It's always a surprise when the stoper comes free. But it usually does.