Have also used the Tamiya R370 without any problem (i.e. the black motor with the size of R280). Good speed for destroyer (1/200), but a bit fast for 1/350 battleships when running in full speed ...
1:200 Destroyer is actually smaller then 1:350 Battleship! Just use whatever you feel good and have fun!
Hope more people will join playing RC battleships no matter the scales!
Tried Tamiya R370 motors (size of R280), with good result, but just a bit fast for 1/350 battleship when running in full speed, for very good for 1/200 destroyers ...