Not sure if this is correct; I havn't experimented with string gauges too much, so someone correct me if I'm wrong. But...
To me, when strings are too loose and rattle too much, it seems like it would make sense to increase string gauge. If you have a large gauge string and a smaller gauge string tune to the same pitch, the string of larger gauge would always be tighter, I would assume.
I have a similar problem with the B- and E- strings on my 6-string bass; whenever I go to really dig into the strings and really aggressively smack them with my fingers (especially when playing notes in succession), they would feel very loose, and it's very hard to pluck them with consistency because the string moved so much. I recently bought a heavier gauge to see if that helps out at all, but I have yet to put them on, ha.
Well, good luck. Hope this helped.
Brian