Chris,
Yes, I felt the player opened up quite a bit after a couple of hundred hours, both the player and the tubes need some time to settle in before you'll really get to hear what it can do. Tuberolling can also bring out more and will allow you to fine tune the sound to your personal preference.
Also, from the time I'm spending with the GS-1 I'm coming to realize that upgrading the headamp can reveal more of what the player is capable of. Of course I still maintain the internal headamp stands up well to other amps in the $500 region. In my opinion you would probably have to spend close to what you paid for the MiniMax to see a significant improvement other than a change in flavor, but my point is, if/when you want to upgrade that path is open to you and it will allow to get even more out of the player.
There shouldn't be any problem driving two phones, one from the MiniMax and one from the Lite. They aren't being driven by the same amp so there is no extra stress on either.
PM me anytime, if the tubes are sold by then we can still talk about them if you like.