Oh - to explain more in detail and add something - the desired result here is to make sure that there is more torque when you are at these higher speeds, so as not to lose the steps mentioned by your pal eubji*. *Sorry I cannot recall the name at the top of my head.
In addition to this, the logic behind wiring the motors this way is to increase the current draw hence to drive the motors with more juice - hence the more torque. I have never heard of anything bad happening because of this.
Now, if you take my advice, prepare to budget for more stuff. First, you will also have to do a makeover of the resistors on the drive - so that you get a ration of 1:1 on the screw drives.
I say this because when you mentioned the godawful ratio on the NEMA, I thought -poor you - you are asking too much from them, if they are still connected in series. Call to my attention if there is anything I have missed.