Would there be any Code issues with using a French 3-way arrangement to control a relay rather than switching the light directly? If not, and if you could find a way to fit the relay at the single-gang box without too much disturbance, that would work.
Failing that, use the diode arrangement to switch a relay. Use two conductors of the 14/3 to take power to the far location and wire the outside light as normal.
Tap the hot to the common terminal of the 3-way, then use a diode from each remaining switch terminal commoned to the remaining wire of the 14/3. One diode should be anode to the "traveler," the other cathode. Use a similar diode arrangement at the other end then take the common of that 3-way to your relay coil.
I'll leave it to the NEC experts to come up with any code objections to this idea.
