Spreadshirt is awesome and not only that, if you hit up their customer support, you can work custom deals.
They dont really dropship, but once you get a decent flow of orders, you should be fine. Just buffer with a longer shipping date + a lower price tag.
Instead of a week, make it 3 weeks and charge them $10 rather than $15 for the shirt. That simple.
Bigger sites like ript and yetee did this to start out to the best of my knowledge, but they turned their profits into a fulltime print shop.