I think part of the trouble that you face is dealing with the "insurance company". Most of those restoration shops are going to be charging more than what the insurance will or would pay a normal body shop in an hourly rate. Reality is insurance companies some how basically dictate what they will pay a shop hourly and unless the shop agrees to work with them, the customer would be out the difference. Most restoration shops will charge what ever their posted rate is per hour, per person for what ever amount of time they invest in your vehicle.
I am guessing that is the reason the one shop mentions the idea of charging for a good estimate. Most of these insurance companies pay a third party independent appraisal person or company to send someone out and all they care about is getting the original estimate written so they can collect for that. Insurance companies know that most claims will have a supplement , but all of that will have to be proven and sent into them with pictures and emails as the work progresses. All of that takes time to do so it will take a shop either willing to do those things, or you can try to get a couple good estimates to begin with and see if they will agree to pay those. It really sucks that this is the way things go but working in a bodyshop for 20 years gives me some experience with this. Reality is they, the "insurance companies" place all of this responsibility on the shop to do today and it really is a pain.
Matt