I think that your appointment with the professor might be very fruitful. She may have good recommendations with regard to where she studied, and/or even considering her recommendations you might just find you feel comfortable and that she naturally falls into the mentor roll.

One thing I neglected to mention last time is do you know why they "strongly discourage" remaining in their grad program? They may have some valid reasons that make sense. Not that that should make your decision, but should be a factor in it, if you think their reasons may have some validity. Also knowing their reasons, if you decide you like this professor you are meeting, maybe you can more easily make a choice as to whether staying there for benefit of having this professor available outweighs whatever reasons they have for not wanting you to continue there.

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