Rear tire size needed for 340 stroker?

Here are my suggestions to you.
I have a Hellwig no.5905 1 1/8'' solid sway bar on the front of my Dart Sport(cousin to the Duster and brother to the Demon...same cars) and love it. It prevents my headers from scrapping on anything, unlike before and many other benefits besides including cornering. I even priced them for you and through Amazon.ca is the cheapest way I found. $270.56 CDN + free shipping. For starters that is the first thing I would get. If you get it from the states there is shipping, duty and exchange which adds up to much more than that unless you are able to pick it up, then all you add is fuel and exchange which still adds up to a higher total.

Then there was the matter of tires:
For front tires I would go with 255/60R15 for the front, if it fits, $150.00 to $155 CDN( that big a tire will be hard to steer) . The biggest 15'' that fits on my Sport is about 205-215/65R15 with a stock front suspension. I run 7'' wheels in front.
And 275/60R15 for the rear $160.00 range...first choice BF Goodrich T/A 2nd choice Cooper Cobra. Both have raised white letters. The 255 is 27'' tall and the 275 is 28'' tall. With big & wide front tires you will likely have to raise your front suspension and maybe require other mods. I have 8'' wheels in back with 255/60r15. If you run 275s in back your gears will have to be in the range of 380-400 to 1.