Nameplate mystery

I decided to tackle removing the motor and beginning the process of rewinding by having a look at the old windings. It turned out that the nameplate was wrong--- It's not a 4-pole motor at all. It is a 2-pole motor, meaning the full-load speed was around 3500 rpm, not 1750 at the nameplate advertised. There are 36 slots in the stator, meaning that 6 slots are used for each pole, times 2 poles, times 3 phases. I would like to increase the number of poles to increase the torque. Rewinding for 4 poles is impossible, as 36 slots divided by 3 phases gives 12. 12 divided by 4 poles gives 3 slots per pole. The number of slots per pole have to be even, though. The number of poles also has to be even, and there are only two even numbers that multiply together to get 12 -- 6 and 2, so this motor has to have to have 6 poles with 2 slots per pole or 2 poles with 6 slots per pole. Two slots per pole isn't enough because it results in a poor approximation of a sinusoidally varying magnetic field around the stator, so I guess I'm stuck with 2 poles. This means that at 180 Hz, the motor is spinning about 10000 rpm, which isn't too good for the transmission, I'm sure.