To fix this I decided to install headphone jacks on each earpiece. This not only fixed the breaking cable, but also acts as a psuedo quick disconnect as well. DISCLAIMER: this instructable will only work if you can open up your headphones ear pieces in such a way that they can be put back together! I have Grado SR60s, which worked perfectly for this.
I didn't think ahead and take a picture of all the tools needed, but here's a list;
• Pliers and/or wire snips
• Cable Strippers
• Dremel Tool and/or Drill + Bits
• 2 x 1/8" micro mono panel mount headphone jacks
• 2 x 1/8" mono phone plugs
• Heat shrink of various sizes and colors.
• Heat gun
NOTE: I've skipped describing the process of how to actually connect the speaker wires to the connectors and plugs. There are other, better, instructables available that describe the process. Sorry!
Step 1: Disassemble Earpieces
Step 2: Install the Headphone Jack
Step 3: Finishing Up
I used heat shrink to not only protect the connected cable by securing it snugly in the connectors outer shield but to also denote which connector is left vs right.
Once that's done, you're good to go!
NOTE: After over a year of use, one of my ear pieces started to fall apart. I had not glued it back in place and did not want to. To fix the problem, I used a post-it note to create a shim to tighten up the two pieces of the ear piece. I ripped the non-sticky part of the note off and stuck the sticky side to the inside portion of the ear piece. I put two pieces on it like this, and now it's tight as can be. I think using electrical tape would be a better option (if a bit too thick), but I only had office supplies on hand.