Isaac,

No doubt some hawks will not do well with any mounting system as you say but I've ignored feathers being out of place and leave the harness on for years. At times feathers are displaced during the molt but eventually they go back down. My 4th year HH and 3 year gos are ending the molt with the original harness at this time with no problem.
I mount them rather loosely so they do not become tight during the molt.

Harry.