Hmmmm.
Bear in mind that:
momentum = chalk while
kinetic energy = cheese Kinetic energy is measured in joules, the unit of
cheese energy, while momentum is measured in kg*m/s (or Newton seconds). A different kettle of fish.
The joules you're burning boils water, and the resulting pressurised steam has kinetic energy (on a molecular level, think of all those hot H
2O molecules bouncing about inside the boiler. Temperature is just a measure of speed). Once released, the steam's kinetic energy is (hopefully) all sent aft. The momentum of the steam is the steam's mass times its velocity, as you say.
To maintain a steady-state of thrust (while acknowledging a slow net loss of water and propane over time) the amount of steam leaving the boiler (i.e. a mass of steam being accelerated from 0 to "v" m/s in the boat's reference frame) must not exceed the energy the burner's putting into the boiler (minus a bit, due to natural inefficiencies) else you'll run out of pressure. So we've obviously got a KE limit.
Maximising the momentum for a limited KE will produce more thrust. As you say, both momentum and KE are dependent on mass and velocity, and maximum momentum
from a given KE suggests a low velocity and a large mass is best. This probably explains why pure steam-rocketry is inefficient: you can't boil water quickly enough for a respectable mass-loss, and the velocity of a released steam jet is automatically high. (This also answers why "chucking a cannon ball" is better than "chucking a marble".)
So, if we've a high-velocity/low-mass jet and would be better with a low-velocity/high-mass jet, I think the answer for more thrust/better efficiency comes down to:
1/ Utilising ambient air or water to increase the mass of the thrust stream (and thereby lower its velocity).
2/ Using a burner big enough to generate lots of steam, then lowering the temperature of this steam (= lowering its velocity) before it goes overboard by using a nozzle to allow the steam to expand down to 1atm.
3/ Both the above.
Andy