Eventually in your racing career, you will grow to learn that tires win races. Everything else being equal, the car with better tires will win. But good tires won't make up for setup problems.
By design and definition, we are handicapped in the tire department on legends cars. This, in part, is a system check to reduce the need to spend big money on small horsepower gains since you already have more engine than the tires can handle.
New tires will out perform older tires. Cut tires will outperform uncut tires. You can use Track Tac's "Tire Tuff" tire conditioner on the tires to help keep them fresh for longer. By using this, you are simply re-introducing the natural conditioners back into the rubber. It is therefore not detectable by so called "sniffers." ARC Racing sells Tire Tuff, as well as all of Track Tac's other great products.
Cutting tires. You can cut them to last, or cut them to be fast. With fast cuts, the outside tires will begin to wear out after about 4 races. With proper care, you can squeeze 2 extra races from them. With cuts made to last, you can get 10 - 15 races before all the good is gone from them. Just because you still have tread on the tires does not mean they are still good. Proper care, such as conditioning, just keeps your tires good for longer.
Cutting tires does a few things. First, it lightens the rotating mass considerably. This helps acceleration. Second, by cutting camber into the tire, it helps the tire roll onto a larger contact patch on the right side and get off the LR tire just enough to help it slip through the turn. Since we have a spooled rear axle and both rear tires have the same rotation, so something has to slip a little or it can cause you to push cutting some stagger into the rear wheel set helps too. The LR needs to be smaller in circumference because it has a smaller circle to travel on the track. Of course, cutting makes the tires round. Out of round tires are not consistent because they hop rather than roll. Not only does that mess up grip, it actually robs power.