Hello Alexander,
Operated various Cessna twins in a previous life, including the 340. (Not the 414, though)
A stretcher would fit in the cabin of the 340, however I'm not sure you could load it through the rather narrow door with a patient in situ. (404's and some 402's had a cargo door adjacent to the stairs, ideal)
I'm not aware of a special tyre kit. The 340 has a mudguard-type deflector installed on the nosewheel which worked fine and the mains never seemed to kick up too much debris, i.e. we never used to pick up flap damage or dents in the leading edges of the tailplane. We operated into all sorts of unpaved strips, i.e. sand, gravel. No issues.
I think some of the Aero Commander piston-twins may have been inflatable, but stand by to be corrected on that one - Adam Frisch, any input?
The 340 is a lovely little thing. The big cowl flaps are particularly good, makes descents a lot less of a hassle for the engines. Not too much of a legal useful load though, if memory serves. A realistic three- to four-seater if you want to go anywhere.
Good luck.
