When you get the urge to bone up on your long range shooting with your 44, may I suggest that you try to find a shooting range that has silhouette matches. Douglas Ridge out in Boring has matches, but not as regular as they used to have. Albany rifle and pistol used to have matches too, but I don't know if they still do. Most big bore matches require you to shoot at known distances form 50 to 200 yards.
As far as a single shot handgun goes Thompson Center has some nice ones, and sometimes you can find one used for a decent price. You can change the caliber by swithching barrels. Many of them can be used with either iron sights or with handgun scopes mounted on them. I own a couple of them and have been quite satisfied with their performance over the last several years.