I once got a 750/1500 rpm (in the 50 hz world) where the client wanted it converted to just 1500 RPM. I found that the stator slots/rotor slots ratio would not allow the motor to start if designed purely for 1500 RPM. To prove the theory right, I rewound the motor to 1500 rpm (at my cost) and sure enough, the motor would not start. So, I changed it back to to 750/1500 RPM. Costly but valuable lesson.
Since your speed ratio is not 2:1, the motor should be having two windings.
So, yes, rewind it for 1800 rpm with more copper as aolalde suggested. It will result in a much cooler motor with a longer life with considerably less losses.
*Why a man thinks he outrun a chasing dog when it has twice as many legs?*