As far as I can tell, this isn't a burning problem by any stretch of the imagination.
Maybe it's just me, but the swapping technique isn't all that different between model 1 and 2. Model 1 gives you a flashing light so you know when to swap, model 2 you need to listen to the sounds. In any event...
Correct me if I'm wrong, but what I think you're doing is leaving the original game in the drive until after the security check is done, then putting in the copy. In which case, that's not how you do it, and I'm surprised you got other games to work (even w/o sound).
So, the first time through, it gets the info on the CD, then finds the label, then starts the game. Here you need to note that after the security check, it's not checking the game again, it's going right into the game. So, if you put VF in and then switch it (without doing the swap properly) then the Saturn is thinking that you're going to play VF, and NOT Nights, or what have you.
In sum, you need to put the copy in, switch in when it wants to check the security ring, and then switch again to play the game. Otherwise, you'll have a lot of problems trying to play anything other than VF. Further, I don't think model 1 makes it that much easier that model 2, but that's just me. It takes a little practice. If anything, you'll have one heck of a time trying to mod that Model 1.
Hope this helps.
EDIT - I just noticed that you were swapping original copies of Nights and the sampler and VF2 in. Not much changes, except when you leave Nights in, the Saturn thinks it's going to play Nights and not VF2. Same w/ the Sampler. You still need to master the swap trick, which is: copy -> original -> copy.