The big issue with a Rear tire going flat as you ride, is the slower speed. At a higher speed you will feel the tire go soft and the rear wiggle a bit, BUT as you get to a very low speed with a flat rear tire, if the bead breaks the rear will wobble back forth and I have seen guys go down trying to get stopped. You already have 9400 miles in it and I am willing to bet that carcass is pretty thin already and not going to hold up well to running soft.

My suggestion is to flip someone a few bucks to help you remove the tire from the bike and get the tire swapped.