Very brave of you to go out-of-network. I considered it, but when I looked at the real costs, I discovered that it was simply not possible.
I made a point at each step to ask. It came up in very unexpected places. For instance my bone scan - hospital equipment, in network; tech, one was, one wasn't, so had to schedule the test to use the right tech. For the evaluation, I actually had to wait longer on the results to get an in-network doctor.
It made each test an exercise in "I wonder what they might be able to charge me for", and checking each and every one.
On the other hand, CT scans get prescribed a lot - you would need to discuss that with the doctor