The best thing I can advise is to do as much internal marketing as you can -- meaning lunchroom, employee meetings, etc. -- to get to know the people on those various projects that need support. If you get to know some of them, and voice your enthusiasm for whatever their particular project is and sort of drop that, gee, your plate hasn't filled up yet and to let you know if there is anything you can do to support their project in your current role, you might find that some of them go to your boss and ask for your time.
And yes, I would advise selective failure on secretarial tasks so you don't get pigeonholed into that role. Sad but true.
Finally, take a look at those administrative tasks -- are they beneath you (like typing someone's edits), or are they "managerial" (like organizing/running meetings)? My DH ended up getting crosswise with one of his female technical people at one point: he thought she was awesome, and so he tried to give her the kind of experience that would put her out there and qualify her to step into management. Which involved a lot of running meetings and running projects and stuff (i.e., logistics and administrative stuff instead of the hard tech she had been doing). Turns out she thought he was overlooking her technical skills and assigning her administrivia because she was a girl -- she had no clue he had identified her for a promotion. And when they did discuss it, it turned out she preferred a purely technical role and didn't actually want to go into management.
Not saying this is necessarily the same thing, but sometimes different people can see the same tasks in different lights, so it may be worth taking a hard look at the types of tasks you are being given as compared to the job description to figure out if it's a bait and switch on their end, or if maybe you thought they meant something different than what they did.
