I had similar issues when working with the North Carolina dataset. Thought some of it may be user error (me). I'm definitely "flying blind" in Global Mapper besides suggestions by you and Joe.
It would actually be nice to work with both heightmaps, with and without vegetation. Maybe start by using with vegetation and plant all significant trees (by hand to control height/depth level, a la garynorman). Then, switch to a heightmap without vegetation, and final contour course, tweak and plant lesser significant vegetation. (Mass planting of trees and then altering heightmap leads to floating trees for me).
Then, outline splines, other CF stuff, retweak contours and terrain paint to finish.
The benefit of "with vegetation" is the ability to "see" trees and heights of trees. I probably would miss the little palmetto by the green without a photo or the heightmap "reminder."

Thanks for your help as well. I should have directly mentioned you earlier. You guys rock! Release date for Kiawah beta is looking more toward Q1 2017. With hand contouring, that was going to be tough on my marriage. While she won't explicitly say so, I am sure my wife thanks you as well. Ignore her "eye rolling".