Mark,
Many gunsmiths will tell you to play with a hand grenade rather than shoot a gun with Twist or Damascus barrels. They may be correct, however many here including me shoot their Twist and Damascus Parkers, LC Smiths, Remingtons etc. all the time. In fact my favorite sporting clays gun is an 1881 lifter Parker with Twist barrels. I've included a picture of it with a mess of dove. I doubt very seriously that your great grandfathers Parker has been messed with ie: the bores honed out to remove pitts. It should be good to go with the proper ammo. There are several manufacurers of shotgun shells appropriate for your Parker. I like
www.rstshells.com because they are easy on the shoulder and gun and preform so wonderfully. I have several #1 frame Parkers and I shoot 7/8 & 1 oz loads as they are very easy on the gun and me.
Good Shooting, Harry