The Contender as a carbine is very light and compact. I too, think it's a dream to carry. If you like to carry your rifle in the crook of your arm, the trigger guard release lever can get in your way. If you're carrying it in both hands, or one hand by the frame, or slung on a shoulder, it will feel like you're carrying a 22 rimfire around.
I have a 16", 18", 20", 21" tapered, and a couple of 23" bull barrels. I think the 20" bulls and the 21" tapered barrels point the best. A close second for me are the 23" bull barrels. I don't find them nose heavy, but I'm using the walnut stock, and not the synthetic stock. I'm also using full size variable scopes on most of them. The synthetic stock is much lighter in weight, and will take away some of the balance at the rear of the carbine. If you're going with a hollow synthetic stock, maybe a shorter barrel would be best. I think the average weight on my carbine, depending on which barrel is on at the time, is around 6 to 6.5 pounds.
Two of my favorite carbine barrels are my 22 lr, and my 6 TCU. Both of which will out shoot most typical bolt action hunting rifles. I DON'T care for the factory butt stock for shooting with a scope. There is not enough comb height for a proper cheek weld, so you end up "floating" up to see through the scope. There are several aftermarket stock options, and I'm planning on one of those myself in the near future.
I hear you on the cost of the conversion, but look at it this way, if you decide to get back out of it, you can easily sell of the carbine parts on the classifieds forums here. Carbine stuff usually sells pretty fast if it's priced well.
You could also just spend some time with your Contender as is, as a .223 handgun. You may be surprised at how accurate one of those can be.