EDIT:
Doh, got distracted...see above! the expert posted while I was messing around.
a couple of thoughts--
When the wood was parted, you've seen how easy it was to penetrate the outer leather. Of course a properly made sheath of heavy leather shouldn't be cut easily, but it will probably have to be considerably thicker leather than that used to cover a scabbard. I think it would weigh more than the scabbard. The wood also probably protects the blade from corrosion than being in contact with leather, if your blades spend a lot of time sheathed. From only canvas? I don't see how, maybe someone else does.
As far as I can tell, the scabbards are made by carving two clamshell like halves of softwood and sewing on wet leather, which shrinks and holds everything together. A few tacks are used to finish the construction around the top. Sometimes the wood warps, or gets split, allowing the blade to slip through.
If you've got a new, softer leather scabbard, you might try something like below. Some older scabbards have leather more like rawhide, and that probably can't be reused.
You might be able to dissasemble the stuff at the top, soak the main sheath in water and pull out two wood pieces. Some of the upper stitching will need to be removed. The two wood pieces can then be dried, glued and/or wrapped so they don't separate again. Or new ones can be made and glued up. They could be wrapped, taped, or constructed with dovetails for extra strength. Then the leather is soaked again and stitched back on. Or new leather is used. If it was me, I try to patch the old leather by gluing on a piece of leather inside and stitching around it before I soaked it and tried to get it back on. Then while the leather is pliable, any remaing gap could be stitched up from the outside.
From the prices I've seen here, the Sarki Shop has very reasonable pricing. That means it's not worth the hassle to mess about yourself, or there's a great reasonably priced backup if/when you screw up your current scabbard. Depends how you look at it.
Uncle's expedient solution is just to lash things up from the outside where the cut is and be done with it.
Terry of the Sarki Shop will probably correct if I've pointed you wrong, he's the expert. I've seen pix of his scabbards and sheaths (without wood). An lots of excellent reviews.