As other noted, perhaps a bit more information would be helpful. For example, what distance(s) are you shooting in F-Class; is it all at 600 yd? What size groups is your setup and load consistently capable of at 100 yd? What velocity and ES/SD values are you obtaining with the 168s? My guess is that your brass may not be the [most] limiting factor. Although they can certainly work at 600 yd, the 168 bullets you're using are going to be subject to greater wind deflection than a higher BC bullet. That can easily include a significant vertical component if the terrain your shooting range is subject to the right wind conditions. However, if you can develop a load that will consistently shoot ~1/2 moa at 100 yd, the 168s will work for MR, no problem.
From the limited information given, I would guess that some improvement in your load development to obtain a more precise and consistent load would be a good place to start. Once you have that, you can work on your form and wind reading with confidence that your bullets are doing their part. If for some reason you cannot develop a load that will shoot in the 1/2 moa range at 100 yd, that might suggest the rifle itself may have some limitations. At that point, a new barrel would make obvious sense. Even without that information, a new barrel chambered for a higher BC bullet such as the 185 Juggernaut is not a huge expense and may not be a bad idea.
The other suggestion I would make is with regard to your optic. This is a place where you could spend some $$$ that wouldn't be wasted, even if you end up with a different rifle at some point. My eyes aren't what they were when i was in my twenties, but they're not bad. I can tell you that 20X magnification is far below where you want to be. You simply can't make as fine a hold with that mag at 600 yd as you could with 32X, 42X, or even 50-60X. It may not seem that important, but it is, and you will be able to tell the difference in your ability to make holds in finer increments immediately when you shoot through a higher power scope. Remember, you can always dial the mag down, but you can't dial it up if it's not there.
Between some improvement in your load development and a scope where you can really discern 1/4 moa (or less) holds on the target, I think you would find a big improvement in your ability to work on your shooting form and wind reading. If you think the brass is a problem at that point, by all means replace it. However, if in the meantime you're still concerned about the brass, you could at least find someone with tools such as a concentricity gauge, or even better, a way to measure case wall thickness. Anything that would allow you to potentially sort and/or cull some of your current brass to improve consistency without having to buy new brass and start over. I would also suggest that using one of a number of possible ways to sort and/or point bullets might also positively impact your consistency. The bottom line is that without a consistent setup/load, improvement in wind reading, form, or anything else, becomes much more challenging.