How to get a very tight tire back on the rim?
The above video shows how to fit a tight tire / rim combination. Although it shows the Marathon Plus tire, it applies to any tire.

The crucial point he makes on the video is that the tire bead doesn't stretch and is the limiting factor in getting the tire on. Thus you need to push the bead into the well of the rim on the sides opposite to the last bit you're trying to get on. Doing this gives you the room you need to get the last bit on.
The extra room will make it easier and you will be less likely to pinch the tube. You can use straps to hold the tire in place if you need to.

I have the Marathon Plus tires and it used to take me an hour of frustration and sore hands trying to get them on. Using the technique in the video it takes me 5 mins like any other tire.