Hello Kicka
First off, no medical practitioner in the UK is EVER incentivised not to treat patients, but I understand the point you are making.
There could be all sorts of reasons why your surgeon has been reluctant to work with you. She may not regard you as a high enough priority over, say mastectomy patients that have cancer or she may regard your condition as cosmetic rather than corrective. It might be that she has little experience of male chest reconstruction and does not want to admit she is not up to the job.
Secondly, you probably know by now that the end result of any cosmetic or corrective procedure cannot be guaranteed. So if she says "There's risk of significant scarring." My response would be "I am well aware of the types and extent of scars that can be made by this surgery. I am also aware that modern techniques in reconstructive surgery minimise the risks of obvious scaring. For example, a crescent shaped incision around the areola is a very discreet way of hiding potential scars" (and produce a picture of a before and after that you have ripped off from this website!)
A concave chest? My response "It is not my expectation for any surgeon to achieve a perfect result. The outcome is down to my personal expectations and how well you [the surgeon] manages that expectation. I also know it comes down to the skill, experience and confidence of the the surgeon that is to perform the work. What confidence do you have in your ability to carry out this kind of work, or is there another surgeon you believe I might be more suited to?"
Be polite, patient and understanding with your surgeon. Show her you know your stuff that you are not afraid to ask her tough questions.
It might be worth going back to this surgeon and find out if she is a) up to the job and b) prepared to cross refer you to another surgeon for a second opinion WHICH YOU ARE ENTITLED TO! Never EVER let anyone fob you off. You have the backing of your GP and now that you are 'in the loop' as it were, you have every chance to reach the end-point you seek.
Hope that helps.