Robert,
It's good to see you trying this...want to offer some of our experience with it in the hope that it might help in some way, as I've been down this road.
John Moore at Mission makes what in my view is the best titanium for knives due to his precipitation hardening process...most other folks that try to harden titanium on their own or through a general commercial heat treater get surface hardened results when they really want a homogenous treatment. Surfarce or spot hardened titanium is misleading when the rubber meets the road.
While Titanium makes for a very cool Tomahawk in terms of light weight and corrosion resistance, it isn't the best tool. Anything one hits with it that is as hard or harder than the titanium itself will result in edge deformation or misalignment. That's where your design skills will come into play considerably...unless the idea is to make the Hawk exclusively a fighter....then, "soft-targets only" allow you to make it thin and sharp, with little regard for durability at the edge because of the design caveat.
We've used forged Beta C as well as surfaced 6AL4V. The Beta is the best, in my opinion.
Good luck and please indeed share the results of your efforts here.