So I picked up a bike for commuting this winter. It has a
Sturmey-Archer 5 speed rear hub. When I bought it the thought didn't
cross my mind that this hub would make it difficult to change the tire
on the side of the road at 5am in 30 degree temps.

I'll probably use something puncture resistant for tires and maybe a sealant.

Basically though to get the tire off means completely disconnecting the cable,
which means my shifts will be out of adjustment. Then the possibility of losing a small part on the side of the road, plus an extra tool I'll have to carry to remove the cable.

It looks like I could maybe get enough slack in the cable to get the cable housing out of the cable stop on the frame and then be able to change the tire with the cable still connected to the hub. Then put the wheel back in the dropouts in the same place it was before the flat...IDK

Anyone have any experience with this?