Masala chai made traditionally is boiled with the tea in it, the spices help cover the tannins and it becomes an accent rather than a detractor in my experience, much like diacetyl in certain styles of beer.
Instead of using "chai tea" from the store, which is more likely to be the cheapest tea dust sprayed with an oil vaguely similar to chai spices in taste, I would get some loose leaf black tea (Assam would be an excellent choice and, AFAIK, traditional), and find a recipe for the traditional stuff with clove, cardamom, cinnamon stick, fresh ginger, etc. (I even throw a couple peppercorns into mine, but that's me...) taking the boil time for the tea recipe and adding the tea ingredients that long before flameout.
If you have a Whole Foods nearby, look for "Rishi" brand chai loose leaf, it's a great brand with the spices already in and no artificial guff.
Excluding the tea to get just the spice would work, but personally I'd try with the tea. I'm not sure how much I would use, however...
Very interested to see how this turns out.