After a lot of testing, having experienced the same as you, I am now able to achieve somewhat of a hover.
Try the following user curve on your axis tune panel for cyclic:
0 2 5 10 18 28 42 57 71 86 100
This works better than any of the standard curvatures. This curve isn't really exponential, it basiscly consists of two linear parts with a smooth transition between them. Try it out and see if it works for you!