This is a long lesson that needs to be done right. Some methods are better than others. It is better suited to a sit around type discussion than anything that can be done here. Liability exposure probably limits a magazine article also.
If you understand the need, the mechanics of cutting the rubber are really pretty easy. You already experienced the difference between a tire sales and repair outfit.
We are actually not alone in that SCCA types also remove some tread mass to reduce the squirm of a full tread when really leaned on in a race. While they want the tread pattern and shape , they just want it reduced to no more than is required for the event.
Recappers also remove tread down to a point but their method is buffing with a wire wheel that leaved it rough for gluing and is not suited for our application.
The amount you remove and the final shape will be determined by the tire design and use. If you remember how a LSR tire works, it will dictate the final shape when underway. Remember it is PSI rather than SIP. Think about a TF rear at speed and that will begin to explain it. Extra attention to the edges is important because the rubber is usually not only thicker there but in the event of a misdirection event (spin), you don't want it to dig in and put the panoramaic top view on the bottom.
A tire truing machine can do a good job and a sharp block plane or even electric will work. One of the things to do during any cutting process to to get a smooth cut. The shape and method of the tooling will produce a distinctive pattern in the surface. The important thing here is to cut it clean and not leave a buffed or ground surface that is more prone to tear away. In metallurgy a rough surface would be called a stress riser, weaken the surface and lead to failure.
Keeping the surface wet with a hand spray bottle of a weak soapy water mix will help the cutter do a better job in any case.
The final OK has to come from the person that signs off the (it works for bikes too) entry. The opinions as well as the skill level will vary as wide as the experience and you may be learning right along with them.
Tune in next week and the featured article will be "How to fly a plane."
Well that is my guess anyway.