Of course you could tie up a spare tube under the brake bridge to the saddle ready to go, then roll the tyre off and switch them over with the wheel in situ.
But really HTFU :D
Fixedwheelnut almost had it. In fact, you'd need to have the spare inner tube looped inside the rear end of the bike. It would end up looping around the non-drive side chainstay and seatstay, effectively running parallel to the seat tube. You could zip tie half a dozen there if you're a really unlucky person. You'd need a sharp knife to a) cut out the old tube each time you punctured; b) cut the zip tie holding the new one. Then you'd just pull it around to the inside of the rear end and put into the wheel. This is such a shit hot idea, I may even write in to Viz!
Fixedwheelnut almost had it. In fact, you'd need to have the spare inner tube looped inside the rear end of the bike. It would end up looping around the non-drive side chainstay and seatstay, effectively running parallel to the seat tube. You could zip tie half a dozen there if you're a really unlucky person. You'd need a sharp knife to a) cut out the old tube each time you punctured; b) cut the zip tie holding the new one. Then you'd just pull it around to the inside of the rear end and put into the wheel. This is such a shit hot idea, I may even write in to Viz!