I chuckled when I read your comments re: repairing the handles on your Leg-O-Mutton case. Three months ago on e-Bay I bid on and won the bid on a 1907 Royale Leg-O-Mutton case. One thing led to another and I took the complete case apart and rebuilt it with a half hide of leather, new brass fittings, a yard of billiard cloth, and 40 yards of waxed thread. I readily admit that a few minor repairs lead to first name relationships at the local Tandy Leather store. The new case is now completed and in total I invested $200 in bits and pieces plus my personal labor at $0.50/hour after I gave myself a raise.
The only items I salvaged are the brass nameplate plus the shell of the case which is made of rolled and varnished paper. If I tackle another case, I'll make the shell out of fiberglas.
If I understand your question; to resew the new handles on your case, you may have to cut through the leather bottom seam and gently spread the bottom of the case to reach and resew the handles (make pilot holes prior to sewing with a Dremel type of drill). Next, hand sew the case bottom back together also using a figure 8 type of stitch, i.e, one piece of waxed thread using two needles. PM me if you have other questions and I'll attempt to help you.