First problem will be acquiring suitable elastic. The stuff you will find in fabric stores will not do the job, and trade suppliers for the real heavy duty stuff are not likely to sell anything less than rolls of 100 feet to 100 yards.
The elastic in the Safariland upside down shoulder holsters is installed at the holster opening and serves to retain the revolver. Elastic passes through openings in the inner and outer holster panels, then between the holster panels and holster linings, and is secured at the holster assembly stitch-line. So, some serious disassembly of the holster itself would be required to install the new elastic, then the challenge will be reassembly to precisely line up the existing stitch-lines (otherwise a new set of stitch-lines will be created that potentially will weaken the holster in use).
Finally, the needles used for stitching leather have a chisel-shaped point to cut cleanly through the leather (standard sewing needles use a rounded point that parts the fibers rather than cutting them). Leather needles will sever the elastic fibers, creating weak points where joined to the leather. That can be overcome by hand-stitching using harness needles, but that is a tedious and time consuming task.
Short version: What you are proposing is probably doable, but will require some difficult to acquire elastic and several hours of very skilled work (i.e.: more labor than would be required to make several holsters from scratch). Such a one-time project is likely to be pretty expensive.