I am sure:
Many have successfully dealt with this as you've built those prize winning cars. Some still lose sight of the importance of this. A model car, carefully researched, built and finished is a real shiny jewel, isn't it. BUT! it somehow doesn't look right because it is sitting in a very tiny ridge in the center of the tire tread!
Now, with the Vinyl tires this can be corrected. First make sure both sides of the tire line up by removing the ridge carefully with the sharpest X-Acto or Excel Blade you have. Sometimes you will find the sides are not quite centered. If it's VERY MINOR Proceed with the next step. If not discard this tire and get another that is in better alignment!
Very carefully, using a number eleven blade tip deepen the tread grooves a wee bit. You must use a magnifier for this. Now, have you done all I have described? Good. Now put the tire on an old wheel mounted on an axle that fits properly. Make sure it is not twisted. Put said wheel and tire assembly in your smallest BATTERY powered electric drill, via the axle and spin VERY SLOWLY. on a piece of 320 grit sandpaper. till it gets a flatter cross section.
Now go to succedingly smaller( finer- grits till it is smooth,) But you carefully preserved the tread pattern. Now take the tire off, mount on your desired wheel and there you have it. Oh! if you wish a little Pucker in the bottom like a radial has then press down on the tire while pouring boiling water on it. This will help creat the Body Weight Pucker you normally see. Want a flat? Do this till it's well, Flat. Do this maneuver while mounted on the old wheel. Because it's a model you might have to warp the chassis a wee bit around the suspension to compensate and create that "Flat Tire Lean". See you around!