Using Wordpress in conjunction with Printmojo?

Big Cartel in conjunction with fulfillment services

Hi there,

I have several designs I am interested in selling on T-shirts
So far I think Big Cartel is a great solution for a good online store that works for me. Here's the problem. I am away from home, often in other countries, most of the year for my career. So as far as printing these shirts and sending them off myself I really can't do that.
Want I would like to do is have some kind of fulfillment service that does screen printing (such as printmojo) send the products for me.
The problem I am facing with this is how do I get the information from Big Cartel to Printmojo. Is it possible to edit the Big Cartel code with the diamond or premium services to have the checkout automatically direct customers to printmojo?
Does anyone have some suggestions? I've looked into services like Wordpress as well and am open to ideas.