I am 6'4" and own a Hennessey. Mitigation is a good choice of word, as I have never been truly able to lie flat, or more than flat, on an outing.
Our height certainly plays a factor, so getting a hammock cut a foot larger would go well for us. I know you (JGGiant) have tried the Warbonnet, and perhaps others, so you needn't the description on what the market has available. I would say that the suspension of your hammock is a vital, and for me, not too easy to explain aspect of how to lay flat. If it is too taut, or too loose, you will be less comfortable. You must find the "Goldilocks Effect" and suspend your cot juuuuussstt riiight.
Additionally, it could be the material of the hammock that throws you off. For example, sleeping on my floor, even when cushioned, does not feel as comfy to me as my bed. When I lay flat in my hammock, it could be that even though I am set up nicely parallel to flat ground, and my suspension is equally placed, my body still smarts from lying on something uncommon and I feel like I am not flat.
Perhaps a hammock with a stretchier material placed strategically at hips, shoulders and heals would be more comfortable? Alas, this is for the MYOG field, a club I do not subscribe to. :)