Really need something in between Versa and Slingshot.  Karma is too strong for what I'm looking for.

Which Karma is too strong?  The purple/pink pearl with a slightly weaker layout should fit there.

I may try another slingshot with a slightly stronger pin position.  Dead above the fingers.  Does not produce much back end.  Perhaps a pin around the 1 or 2 o'clock position will help it to turn over a little more.

Yes, it will, for the average PAP, that pin is very weak.

But, Not which Slingshot, but which Karma?

The new Brunswick Meanstreak would fill that gap perfectly, http://www.bowlwithbrunswick.com/balls/detail/meanstreak/ . It is a higher RG ball than the C*(System) versa-max which will get it down the lane a little farther. With the pearlized coverstock and polish, it will recover quicker when reaching the friction.