Wow, it sounds like you really understand the BlueCard rules. Explain this: most of the employer groups have PPO or are self insured, which means they have out of network benefits. Generally, being out of network pays more. So you are saying you would rather pay more? (Then create an admistrative nightmare to patients, doctors, claims and network people). I've seen that some network people calling doctors, does that make sense? Someone should do a cost benefit on this practice. In most states, the Blues are on equal footing with the national Plans, therefore redirection efforts are usually unsuccessful. But good luck.
This doesn't address the fact that physicians have selected a lab based on the information it provides for their patients. The health plan is only to manage benefits and costs. My guess at the end of the year your lab costs will have increased because of the out of network payments. Also, you'll get tired of the national labs calling you every day because they want you to call an office on their behalf. (Insead of competing on products and service).