One way of shortening the cycle of iterations with a new printing shop is to get a profiling unit for printers, if you don't already have one. Send a prospective supplier the test patch file for printing and create the profile from what they send you as prints. Photo Shop allows using any profile loaded on your computer for soft-proofing which will give a very good idea of what the prints will be like. Have done this my local printers and it works very well for prints larger than my printer can handle. As a bonus, the test patches were printed for free. They appreciate it when their customers want to create profiles for printing with them.