I searched for Arduino Uno motor shields for more than two stepper motors, but couldn't find any.
There are plenty of non-shield options that drive one stepper each. Connecting 4 or more of them to one Arduino is easy.
I have decided to go another simpler route: two stepper motors w/ timing pulleys and belts. With that said, I don't believe I'll be needing to hire anymore.
I think Rube Goldberg tried that. I wish you better luck.