Keith,
Your 'cylinder' simplification takes us right back to this ancient picture (sorry, only a scribble on-the-fly)..
Where does the thrust come from? From the pressure/force on the left side, which is not compensated by an equivalent pressure/force on the right.
Now if this were a proper rocket, with a con-di nozzle, and enough chamber pressure for the throat to go Mach 1, you'd get some additional thrust from the expansion in the nozzle (why does the shuttle engine have those large bell nozzles? It does help ...).
CJ