If the Closing Disclosure needs to go out to meet the timing requirements, I would look to Comment #2 under §1026.19(f)(1)(i) and the ability to estimate based on the best information reasonably available. It gives some examples on meeting the "reasonably available" standard. For example, it says just disclosing an estimate without trying to request the actual charge is not okay. If you're contacting the provider and they just won't give you the information (or possibly don't know for whatever reason) and the disclosure needs to go out, I feel you've done you're due diligence. Make sure your efforts are documented. I'm not sure what else you can do on that specific transaction. Here is part of that comment:
"ii. Estimates. If an actual term is unknown, the creditor may utilize estimates using the best information reasonably available in making disclosures even though the creditor knows that more precise information will be available at or before consummation. However, the creditor may not utilize an estimate without exercising due diligence to obtain the actual term for the consumer's transaction."
If you're only trying to get the cost way early in the process, just to get the disclosure out to mark it off your list, that's a different issue.