Find out who is going to do your surgery. Are you from North America? I can only assume that you will not be booked for surgery until the surgeon that intends to carry out your work has evaluated your condition.
As and when you meet him or her, it is imperative you ask about their past experience with this kind of procedure. Ask them what they have typically dealt with in the past, how they managed their patients expectations and what kind of outcomes came about. Ask to see before and after pictures of their work for this kind of surgery to help you understand what you can expect.
If you feel that the surgeon in question lacks experience or skill in dealing with male chest reduction/sculpture, then you must decide if they are for you or not. In the UK, where surgery is sometimes free via the government health system (the NHS or National Health Service) if the patient and his family doctor agree that the initial surgeon is not best suited for this kind of procedure, then the patient is entitled to be referred to another surgeon who is. Will you be given any kind of option in this respect? Also in the UK the NHS surgeons typically mostly deal with female breast mastectomies, reductions and augmentations. Male chest reduction often takes as little as 5% of their annual caseload which amounts to less than half a dozen MCRs a year - which was not enough by my standards, so I went private.
If after finding out the above you are still not satisfied, I urge you to find out about private surgeons you are able to travel to to carry out the work that is needed. I appreciate the lure of getting it done via insurance, but this is a life-changing operation and it's essential you do your homework and get it right first time as second chances are a hassle and increase the risk of reconstructive complexities.
In the grand scheme of things, paying a few thousand pounds to get it right first time is in fact quite cheap.
Hope that helps.