I think it's typical for MA programs, particularly those with a thesis component, to feel somewhat rushed. Because you are more than likely going to be moving on to another institution, and since your prospective mentors have a billion other time commitments and probably several other grad students, yeah, you're likely not their first priority. I really don't think that should be too much of a concern. Your using the time in an MA program to sharpen your skills, broaden you reading, and see through to completion an extended and concentrated intellectual project. All that being said, a thesis isn't a diss, and no one expects it be an original contribution to the field. It doesn't require the kind of mentor/faculty attention that a diss necessarily does.
If you want to get the most out of the faculty members you choose to work with, there are a few things you can do. Obviously, you're going to want to take some classes with faculty you're interested in. But also try to narrow your interests as quickly as possible and make every assignment / term paper / writing situation something that works toward your larger project. As an example, imagine you take two classes with your thesis advisor during your MA. You write two papers that become chapters of your thesis or at least significantly develop some kind of idea crucial to your thesis. The faculty member obviously reads and responds to these for the class, but will also read them again and in their various iterations while you're assembling and drafting your thesis. They will be privy to the flow of your ideas and changes in your writing, and all told will probably end up reading your work four or five times before you are ready to defend.
Also, if there's a faculty member you like and can work with that is new to the tenure track, that would also be ideal if you want extra attention. This is what I did, and while my advisor was involved with several theses / diss', they were only directing mine.