PDD, following is another thought on sewing the leather to secure the handle strap. Most of the Leg-O-Mutton cases have the barrel and action divider hinged at the end opposite the cap. If so, move the divider down from the opening side of the case to give you more room. Drill holes around the exterior of the leather securing patches from the top of case side through both the patches and the case. Use a drill a little larger in size so that two needles can pass through the common hole. If you have enough room in your case to allow your hand to reach in to manipulate the needles, great - you may have to use needle nosed pliers to grab the needles inside the case.
Using the one waxed thread with the two needles attached, start the sewing process by running half of the thread length down through the first strap hole. Next, take the top needle and partially run the needle through the second oversized hole. Using this first needle as a guide, run the second needle up through the hole and carefully pull both needles/thread to secure the figure 8 type of loop. Continue the process around the other predrilled holes until the sewing is complete - stop and pour yourself a Scotch, you earned it!