So far it's going pretty well. Example gif below:

I saved the animation of the character on the left and loaded it onto the characters on the right. (the reason the front arm deforms on the middle character is I used some point animation on the original characters arm which, obviously, isn't saved/loaded)
The way it works right now is the script only saves animation from named bones and loads it onto bones with the same name. So for example, these three characters front arms consist of bones named "upper front arm", "lower front arm", "front hand" and so on.
It will save animation between the start and end frames of the projects and right now it can only save/load rotation and position, so no keyframe interpolation, cycling, scale e.t.c.
Now before I spend more time on this I want to make sure that no such script has already been done. Has it? Because this could take some effort to make really good and I'd rather not do unnecessary work.
If you want to play with it you can download it here: http://dauid.com/tools/scripts/loadsaveboneanim.zip
But remember:
*It's still in very early development.
*You have to name the bones whose animation you want to save/load.
*It won't work if the characters were created facing different directions:

*Right now named bones have to have unique names
*It's a menu script so put it in the anime studio/scripts/menu/third party folder. For example, on my system the path is C:\Program Files (x86)\Smith Micro\Anime Studio Pro 7\scripts\menu\Third Party
Things I'm hoping to be able to do:
*Save/load more data. Cycling, scale, key interpolation, bone locking e.t.c.
*The option to load animation into an action.
*Not requiring unique names (for example being able to load a two legged animation onto a four legged character)
*Load animation between characters facing different directions