For example:


  The word rarely turns up outside of those contexts.
  
  The word turns up rarely outside of those contexts.


Which one is correct and why?


Question: Is there a way to put a copy rotation constraint with an influence higher than 1?
Answer: Use F-Curve Drivers.

https://www.youtube.com/watch?v=jMoBFzXFAUM

Use a scripted expression on the OWNER object's driver with the Target object set. By animating the TARGET object, the OWNER responds accordingly to the driver. 

Eg: Two Cubes, CubeA and CubeB:


Add SINGLE DRIVER to CubeB's x rotation transform box.   
Go to Graph window.
Change from F-Curveto Drivers.
Select it's X Rotation in the list on left side.
Scroll down in the right side panel to find Drivers.
Set Ob to CubeA Change Type to X Rotation (since we added single drive to x rotation).
In the field under Script Expression:
Delete 0.00 and write var * 2 (var is the name of variable box we
changed the ob/type in).


Now rotate on CubeA's x axis. CubeB rotates on the x axis at twice the speed.

Using this method, you will never have that 179-180 problem.