Since the space still exists under the rear deck but is too small for a spare, get a 12 volt air compressor, jack, lug wrench (they don't give you one) and a tire plug kit.
The commonly accepted myth is that run flat tires cannot be repaired under any conditions...none... not at all.. if you get a nail in the center of the tread then you need a new tire.. That is not true.
Look up the details on the tire manufacturers web sites; some do allow repairs with a few caveats;
1) The tire cannot be driven on while flat. It still must have at least 15 psi while driving on it. Driving on run-flat tires is very hard on the sidewalls of the tires, they heat up and the stresses begin to break down the belts.
2) The repair cannot be anywhere near the sidewall.
So, if you are zipping along on the highway and suddenly get a low pressure warning on one tire you need to pull over immediately and get air back in to that tire. Do not let the pressure drop all the way down while the car is moving.
The tire can be patched (ideal) or plugged (less than ideal, and it depends upon the method). Tire shops may not like working on run-flats because they have a different bead design and are very difficult to break the bead (when removing the tire).
Personally, I carry a plug kit, jack, air compressor, lug wrench and a bottle of soapy water.
Some of this can be done on the vehicle, find the hole (probably a nail or screw still stuck in it) and depending upon how much of a hole I will remove the object and insert 1-2 plugs. Then put the tire at full pressure and squirt soapy water to see if bubbles form, that would indicate that the plug has not completely filled the hole.
What I use is this;
Dynaplug® Online Store | Dynaplug® Pro Xtreme - Tubeless Tire Repair Kit
I have plugged tires in the field before. If you do off-roading or own an ATV where you are going to be away from facilities its always a good idea to carry a tire repair kit.
At the worst, you are out the cost of the little rubber plugs that get inserted in to the tire. At the best it saves you $250- $400 for the cost of a new tire. Maybe when you are in some really remote area where they do not stock run-flat tires and you have to wait for a day for a new one to arrive.