There is a program called
Sidewindow that might do what you want.
I've never tried it and I'm not sure if it is up to date.
I might give it a try when I have a bit of time and let you know but if you get to try it first I'd be happy to hear if it works.
Edit: I just tried it, it works fine on an X51v running L11 6.1
You can certainly drag anything on your main monitor to the Ax.
I'll check it out a bit more thoroughly tomorrow.
Edit: Sorry, I just noticed you tried side window already.