They have a press release here.
It contains the selections (listed below), and the grant amounts. "Tactical" means grants up to \$100k and "Strategic" grants up to \$250k.
Directed Energy for Revolutionary Space Propulsion and Power Projection (STRATEGIC): Modular and scalable directed energy approach with propulsion applications ranging ...
Several possibilities, not all of which use the water directly
arcjets, resistojets, etc can use superheated steam as exhaust though this does not get very good ISP.
similarly it is possible to run an NTR on water vapor though this gets worse performance than a chemical rocket.
some types of ion or plasma electrical thrusters can be made to use water as ...
Unit of impulse is newton-sec and not newton/sec and it is not equal to thrust because you are not going to accelerate all the ions in duration of 1 sec. Therefore, if it takes more than 1 sec then your thrust would be lesser than your calculated impulse value.
One more option was the Kickstarter project CAT: A Thruster for Interplanetary CubeSats (unsuccessfully funded), in which had been supposed to use water or iodine as propellant for the plasma thruster.
CAT = Cubesat Ambipolar Thruster, an ion thruster technology capable of using several types of propellants that can be gases as low pressure. This flexibility ...
NASA TM-78661 TECHNIOUES
FOR THE DETERMINATION
TRANSPORTATION SYSTEMS agrees with the "proportional" method
Main propulsion system tank mass, if non integral, is much more
sensitive to vehicle physical size and varies as Lr3 or directly as
propellant mass since tank mass is approximately equal to a constant
RP-1 Was Adopted By The Military Because It's Storable, Temperature-Insensitive, and Similar To Jet Fuel
According to Clarks' Ignition, the adoption of RP-1 rocket kerosene as the standard fuel for hydrocarbon rockets was very much a result of military concerns, including logistics, but it was a bit more complicated than you described.
To summarize Clark:
Rockets frequently (potentially even usually) are not operated stoichiometrically, as this tends not to be the most efficient operating point.
The most extreme example is that of the H2/O2 rocket, which is normally run very rich so that the exhaust contains a lot of unburned hydrogen -- this reduces the burning temperature and the very light hydrogen ...