I really would love to buy a StackOverflow T-Shirt, and I guess I'm not alone.
In the first I thought about to limit it so a reputation could to avoid a overrun to your shop, but I read that you "only averaged maybe $20-$50 a day in sales". So this limit does not make sense. But it would be a great thing for getting more rep ;-)
I think it should be possible to create a simple wait list formula, where you could hoarding the orders and send the order out once in quarter. That would solve your logistic problems and possible lower your shipping costs.
I really have no problem to wait some month for one StackOverflow T-Shirt as long I would get one.
However I read that you also give them away on some special events. Do you have such events even in Europe? Might be also in Germany?