There shouldn't be anything to stop you trying heavier gauge strings on your Variax.  You should notice some difference in tone in much the same way you would on a standard guitar. The difference in sound might not be as pronounced though, although for the acoustic models I think it should enhance the feel and the sound.  If you have a hard-tail 700 you should be reasonably OK as it is with maybe just a slight tweak to the truss rod to compensate for the greater string tension, but with the trem version you will also need to adjust the trem springs and maybe add another spring or two.

I would suggest going for the thicker strings, as thick as possible IMHO. If you are still finding it not sounding good enough to you, you could try acoustic steel strings. However, that would obviously compromise the electric guitar model tones...