It's been a while, but a few suggestions:
DHL has always seemed to be less expensive than the other major carriers in my experience.
A major transmission rebuilder here in the U.S., Sun Valley, uses large plastic storage containers reinforced with plywood for transmissions. I've also seen large coolers used as well.
If you're shipping something that's on a pallet or is large/heavy/bulky, ask if you can go "space available". If you're not in a hurry this can save a considerable amount of money. You don't get a lower level of service, you just get it on the plane when they have space for it. The last two times I did this (from EU to US using DHL) both shipments went in under a week.
Picking up at the terminal on the receiving end can cut the price, too. That "last mile" can get expensive, especially if you want it unloaded. If terminal pickup isn't an option, try to stick with "tailgate unload" if at all possible. This means there will have to be a way to get it off the truck at the destination, but again, carriers often charge a premium for lift gate delivery.
Good luck!
Dan
