I have been mulling similar ideas. Let me inject this little thought: what is the point of cooking outside vs inside? For us, we don’t like food smells inside and we don’t like to go outside to cook when cold/windy etc. So the reality is that for us, cooking FOOD (real meals) can be done only outside, and making COFFEE and soup and other simple quick stuff can be done inside. THEREFORE, two stoves can be implemented, a bigger kitchen model folds up or slides in low on the door cab, or the door itself, and a smaller coffee burner can be permanently mounted up higher just inside the door. Cook tops are cheap enough and compact enough that it doesn’t have to be complicated, just use two for the two different modes. That also gives the option of running extra burners while cooking to heat water or make cocoa etc.
Or another idea is just make the stove loose and able to move positions.