Did you ever treat the leather with saddle soap or other material?
If you consider replacing them, I will suggest double thick, quality bridle leather, twice or three times as wide, for a really strong carry strap; a narrow, single thickness width will no be comfortable if the leather is doubled and no increased; also have the strap edges rounded for comfort as well.
You could also make your own by sourcing the leather in single thicknesses and having a local luggage repair shop, or saddle maker, (expensive) put them together, with waxed #4 linen cord, or better.
You can also get the leather worker to replace the case lugs and leather pieces that hold them at the same time.
For extended trips with leather straps, bags, etc, you also might consider buying a Harbor Freight leather/canvas stitching tool, and some small rolls of cordage, linen, or hemp or artificial sinew, just in case something gives and you need to repair it yourself.
I wear a Filson Belt made of vegetable tanned, double thick bridle leather, and other than lightly coloured stretch markings, think it's good for another 20-25 years as a casual and utility everyday belt.