Have you costed out the difference? You know how much of everything it takes, so make two lists. List everything, even the things that don't change, like the thread for the long arm (only way to see how much you could save on material). Compare the two lists of your costs. You may find there's not a whole lot of difference in the two lists. My guess is less than $40.00.
I don't know if this is a viable idea or not. What if you had them prep the tee shirts? (I've not made a t-shirt quilt, so all this is conjecture.) If they think it costs too much money, give them part of the labor (and costs). Make up a tutorial on how to cut the shirts (or copy one off the net) , what kind of fusible to buy and how to do it. (anybody can iron) Make sure they make the squares large enough for you to square them up afterwards to your standard size.
You could also have a standard pattern/color for the sashing, binding and backing. You could have a standard number of t-shirts, so everyone is the same. That way you would have less waste. I think you could buy 100% cotton from some where like Marshall Dry Goods pretty cheap. It won't have as nice a hand, but handles just fine. They also have some of the really wide backing stuff, so you save that construction time. You might even have enough scraps from the backing to do the binding.
If you don't do anything special, by that I mean everything on the "ABC" quilt is standard, you might be able to make some money and sell some quilts. The rule is STANDARD - nothing different and no hand work. You'll get bored with it, but that's about the only way you can make any money. If they start to do the, "could you just add this?" or, "can we make this red?". You say of course you can, but it will no longer be the "ABC" quilt. It becomes your custom "XYZ" quilt and costs "a little" more.
It's just an idea. It might not work. It might, though.
bkay