Also have to say that most non-gaited farriers do not leave enough heel on the horses. It's not just a matter of toe length for breakover, but having enough heel and some are quite slow to grow heel. Very easy to 'just take a pass with the rasp' and undo months worth of hard-won growth. But prior posters are correct -- shoe the horse, not the gait.
Not sure I entirely agree with the conformation comments, but that may be a breed-specific thing. I have a mare with a very peculiar conformation who gaits, gaits fino and can gait fino naturally for hours. I think it's less conformation than collection. We get a fair number of horses in for training where they are not gaiting because they are not travelling in a collected frame. If you do not engage the rear end, you don't get gait, at least with Pasos.
Is there a breed group in your area that you can connect with? Someone who can help you shorten the forensic process?