That shotgun should do a great job of slammin' whitetails for ya. Of course, it's pretty much all of us here in IL have ever been able to use. As mentioned above, you could purchase a rifled choke or simply use your imporved cylinder. Make sure in a smoothbore barrel you use a traditional rifled slug or "Foster type" slug. Of the many different slugs from Remington, Breneke, Federal, and Winchester, it has been the Winchester Super-X slugs that have consistently proved the be the best grouping and does an excellent job of cleanly harvesting deer out to 75 to 100 yards. It is unfortunate though that you can't afford to add a fully rifle cantilever barrel with optics,.... then it's a new game!
Personally, because of such limited weapon restrictions here, I choose to carry a T/C Encore Pro Hunter 209x.50 muzzleloader that will shoot circles around ANY slug gun.
Good luck and good shootin'