The main issue is your buy price. $200.00 For a whole sheep (I'm presuming completely undressed... straight from the slaughterhouse), is excessive. I'd have thought you might be able to find farmers willing to sell to you and cut out the middle man. Failing that, a supplier that will give you a better price for a whole carcass that they do not have to cut down.
Another issue is the trimmings. If you are not doing this already, I'd recommend serving lamb burgers, and putting a premium price on those. It's also common in Australia to make lamb burgers with 50% beef mince for those that like a milder flavour. Certainly worth thinking about... that is if you serve burgers. Also, sausages are definately something to think about... as long as you can get a return from what you consider "waste" then that will relieve the issue of having to get such a high price from the choice cuts.
Finally... this totally depends on how you are preparing the larger cuts... It is common to "seal in the juices" with lamb by browning in a skillet or large dutch oven over a stove, even for large cuts like a whole unboned leg or shoulder. This prevents the lamb from drying out and you would get a little better yeild.
The issue you may face is that sealing the juices IN, will also seal the smoke OUT.. In my experience, lamb and mutton takes smoke pretty well, but that is not a commonly shared opinion. It might be worth trying this for some select cuts if you're not actually serving the lamb as a whole BBQ'd animal.
Finally, you can pad out the quantity of lamb you serve per dish by adding different styles of lamb dishes, like souvlaki etc, where the lamb is wrapped with salad and sauces in a flat bread. You can still charge a lot for that, have your clients well fed and full, and also have them remark on the new flavours that this style of dish can provide.
I hope it works out for you. I'm really encouraged that you're serving lamb / mutton in a BBQ restaurant.
Keep up the good work!