I can answer this from experimental observation.
The video slots, such as Thunderstruck, are independent of each other over the 5 skins. This can be shown by the following experiment.
1) Play at Bella, and note ending reel positions.
2) Log into Grand Bay (for example, could be any of the others), and note the reels are in a different position.
3) Log back into Bella, and you will see the reels back at the original position.
If still unsure, play until free spins is triggered, and then attempt to play them out in another of the skins, YOU CAN'T, therefore, the slots are independent, so if you are concerned about the continuation of bad streaks, swap skins and try the slot elsewhere.
The position is a little different with the three reel slots, don't ask me why.
Try this.
Play Diamond Deal until you collect, say, two segments. Now, log into a different skin, you will find the two segments are carried over to ALL FIVE SKINS!!!! HOWEVER, apart from this, the slot main game is just as independent between skins as Thunderstruck, so that if Diamond Deal is playing badly at one, swapping skins may still help (if you believe in MG streaks).
This slot can also trigger a peculiar MG error, so this is A BUG in the software, it is NOT SUPPOSED TO HAPPEN. It is related to the manipulator that brought MiniVegas into disrepute over claims of "illegitimate play". MG fixed the manipulator side of the bug, but left some residual "bad code" in place that still affects Grand Prive because they use this "group" system that is currently unique to them.