Ok. 2 things jump out at me from your post
1. You're in the USA I'm guessing? So you pay good money to see that Dr and he needs to work with you. It's true that there are other meds out there for you that might not cause as much of an issue with your weight...although I have to say all antipsychotics do cause weight gain. Still, the point remains valid that if your Dr is unwilling to work with you to try then you might want to consider changing your Dr. Is there one in your area that has a good reputation?
If you need antipsychotics though changing or reducing meds has got to be done with a trustworthy Dr. Your mental health is priceless. And the fact that your mental health is suffering should be a good enough reason to try a different regime.
2. Antipsychotics are so notorious for weight gain because they increase blood glucose levels quite dramatically. You mentioned you eat mainly protein and veg so I would be tempted to pursue that further and eat high FAT rather than high protein - a true ketogenic diet. Full disclosure I am a
massive fan of ketogenic diets but the point here is that fat releases very very little glucose and therefore insulin so has minimal impact on weight when eaten in the absence of carbs. High fat diets have also been shown to be good for mental health - omega 3s seem to be particularly important. Yes exercise is very important and a great mood booster for some but diet will have the most impact on your weight. To quote the amazing Dr. Aseem Malhotra "You can't outrun a bad diet." I hope your Dr. does see how important this is to your wellbeing to work with you. Good luck