Of course motorcycle gloves in this circumstance are not suitable.
Nichrome wire at this resistance would be either very long or vey thin.
Electric socks cut up is a good idea, you have something allready designed for a similar app.
Take care with 18650 cells, all the ones I've seen have had some protection electronics in the base, this might shutdown the battery on overcurrent, 250ma on the other hand shouldnt be an issue, led torches can take way more than that.
I use my bicycle in cold weather too, fortunately I dont need heated gloves yet, a supplier near me listed 'outdoor heated gloves' in their specials section a while back, these were aa powered maybe more on youur lines, dunno how long the cells would last though, like you said probably not long.
Stiching a battery to the back of the glove would remove awkward wires.