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My problem lies in finding such a company. Cafe Press or similar sites will prevent us from keeping customers on our site and significantly cut into potential profits. | |  | |  | |
I think that may be the problem. You should definitely expect your profits to be cut into when you aren't doing all the work. You trade profit for convenience and less hassle.
I would take another look at the existing companies and see what options are out there. I know you can host your products on your site with CafePress. There are people doing that right now (software developers have made that eaiser).
I think once you realize that the profits will definitely be lower since you're not doing all the printing, warehousing, etc, a lot more options will be open to you.