Had an offline discussion with a good friend (and extremely talented aerospace engineer):

[Friend]

Here's my two cents: I'd go with your venturi design. I think you'll have better luck pulling air through the motor in the same direction the propeller is pushing the air (if only for the top motor). The nozzles you had pictured in your post looked cool, but I don't think they'll help you too much because your flow field probably looks something like this: https://forum.solidworks.com/servlet/JiveServlet/showImage/2-373006-92361/Untitled.png

From my understanding, those nozzles are meant to have the follow go straight into them (like within a pipe or at the very front of an airplane). Your down-wash is going to be going all kinds of unpredictable directions. I'd just leave open slots and let the high velocity (low pressure) air go through the slots pulling the air near the motor through, helping to cool it. How big should the slots be? Maybe 1/3 the radius? There's a trade-off there. Too big and you lose structural strength. Too small and you'll get no cooling air flowing. There's also going to be some unquantifiable lift penalty. I'm not sure if lift is already an issue for GimbalBot or not.

You were right about the velocity increasing on the post-propeller flow as you go out radially. I think it would look more like part (b) of this picture though: http://energyresources.asmedigitalcollection.asme.org/data/Journals/JERTD2/26499/009104j.1.jpeg

The twist on airplane propellers is usually set based on the maximum lift to drag ratio for a certain flight speed and/or throttle setting; not to achieve a uniform down-wash velocity profile like pointyointment implied. Not sure how much thought was put in to your propeller twist by the manufacturer, but it's probably pretty good. 

Good luck Zach! I'm excited to watch how GimbalBot progresses!