Excellent post genka!
I have the earbud baseplate. A buddy and I both broke ours on the same trip: where the flexible rubber mold meets the hard plastic body of the baseplate. So I foresee this eventually being a problem for most users with this type of baseplate.
Unfortunately, I don't have a pic prior to disassembly. Here, I dissected the soft rubber cover to see what I was dealing with.
My buddy approached it a bit differently by replacing the output and relocating it to the bottom of the baseplate. He did an excellent repair but I was stuck on the same idea that genka had.
I simply reused the broken wires
and jumpered the normal output to the appropriate sides on the fixed audio jack. However, I did replace the ground with a shielded wire.
Note that the right channel is not visible because it's under the ground wire. And I didn't have to add the 75 Ω resistors because they were already there.
Fortunately, I found this thread before attacking. Already knowing which traces to cut (to keep from shorting the aux in with the earbud out) saved me some time.
My observations of repurposing the aux in as the earbud output:
1. It's difficult to locate the new output in everyday use; with the baseplate mounted to the side of your head and motorcycle gloves on.
2. The microphone wire needs to be routed with attention so that it does not get in the way while plugging in the headphones.