What I do deny is that Mary's Room demonstrates that such information exists, or that they are justified in believing anything different after being exposed to MR than before.

No, it doens't demonstrate it like a mathematical proof. It isn't intended to work that way. it is supposed to be an intuition pump.

Conversely, if I don't believe that to start with, it might not. "Oh look," I might say, "there's Mary, who knows everything there is to know about color, and has probably therefore had vivid dreams of seeing color as her brain has made various connections with that information, so clearly seeing a yellow banana is not new information to her, therefore etc. etc."

To have dreams of colour is to be in the brain state. So you are not saying Mary would have the information of what yellow looks like without ever having been in a seeing-yellow state. These kind of loophole-finding objections are rather pointless because you can always add riders to thought experiment to block them: Marys skin has been bleached,s he has been given driugs to prevent dreaming, etc.

There might be good reasons to reject that second intuition and embrace the first, or vice-versa,

If we have reasons for an intuition, it isn't an intuition.

All of that said, I certainly agree that there exist experiences which depend on certain classes of brain states to instantiate them, and that in the absence of those brain states those experiences are not possible.

But that isn;t relevant. What is relevant is whether personally instantiating a state is necessary to understand something.