I just thought of that today, maybe that my barrel isn’t thick enough.What's your barrel contour? I believe you need about 0.70"-0.75" at the muzzle for 5/8x24 and this probably depends on the type brake used.
What action is are you shooting? I would not use a machine shop. If they can't do it with the barrel in the action they need a barrel vice and an action wrench.
Don't stay in OKC just because you want to stay in OKC. Get it done right the first time by a quality gun smith. Jon Beanland in Gould OK is an excellent smith, give him a call or email. He's a one man shop so getting ahold of him may take awhile. http://beanlandrifles.com/