For Insurance Law Attorneys there are two other aspects that are important in the case. 1) opposing counsel and 2) your client.
The relationship with the insurance company lawyer makes a difference as far as how smoothly the case is processed. Most of the lawyers involved on both sides in first-party insurance cases will have dealt with each other in other cases.
One way of making the case proceed more smoothly for both of you and your clients is getting on the phone and talking to the lawyer. This happens less with the use of email communications but talking on the phone is much more productive and a good way to work out disputes without having a Judge work it out for you. Getting in front of a Judge is going to cost more money and there is no assurance of the result.