UPDATE ALERT!
So after a very long 11 months I finally got around to doing this mod... well, actually my friend, who's a recording engineer and much handier than I am, did the soldering. The switch and output jack wiring is densely arranged and tucked very tightly under the power indicator lamp assembly and I don't trust my ham fisted soldering skills to get the job done without at least a minor disaster. I took the KX-100 over to his shop, opened everything up and showed him exactly where the operation was to be performed, aided by a screenshot from the assembly manual I downloaded off hifiengine.com. We swapped out the 330 ohm resistors for 60 ohm, which, by my calculation, raises the effective wattage of the headphone output from a very low 23 mW up to about 500 mW. I also had him reverse the connection of the resistors so the headphone jack would finally be wired correctly.
So I finally have this beautiful thing operating more or less in line with modern headphone amps, (at least in terms of power), so I can enjoy the all tubey, gooey goodness from the legendary fisher headphone output we all know and love, even with low sensitivity cans like these amazing Audeze LCD-5s. I recommend it if you also have low sensitivity headphones and have great soldering skills like my friend or have someone you know who can pull it off for you.
One caveat: there's a hum on the left channel that can be noticeable now, depending on how high I have the volume turned up, due to the higher output on the headphone jack. So I may now need to sort that out at some point...