Agree, absolutely don't get a genioplasty on its own.
Edit - Reading back through your posts, it seems that you're from the UK. Given what you've been told, this doesn't surprise me. You won't get the surgery you need here I don't think. Have you expanded your search to Europe? You deserve the best outcome.
Also, 40s is not too old for jaw surgery!
There are 70 year olds who get it done. Don't take those remarks as the absolute truth. These surgeons aren't comfortable in handling your case and are making excuses
("long roots?")
I had a SG with a long, retruded face and it worsened my situation substantially. It just doesn't work when the occlusal plane is so steep.
(PS - I don't know what it is about UK society but I think we're rather ageist compared to others).
Unfortunately, that mandible angle is too steep for genio to be much use. It might improve your situation, but it might also result in a deep, unnatural labiomental fold. What you truly need is a pretty significant CCW rotation. At least that's what I see. Did you see an orthognatic surgeon for opinion?