Update: Ok, adding the Clone virtual machine right to my existing Service Account for View did the trick. I guess I'm a little confused:
Yesterday in my world, I only had a View environment. As such, that had a service account that tied into VCenter with the specific role/rights to deploying VMs in our View environment. Perfect. All is well in the world.
Today, we prop up Composer, and the documentation says we should create a service account for this guy and give him specific role/rights. No problem, we do. We hit the issue I posted originally, and the fix is modifying our View service account's rights. So I guess I have to ask, am I misunderstanding the documentation? Should we have 1 service account/role for View/Composer?
Thanks in advance for THIS portion of the topic.