First, to be honest with you, if you plan on making this a lifestyle, then you should learn to live with (and enjoy) soreness as a part of life.
Sure, there are things that you can do to minimize soreness and some people have naturally better recovery abilities than others. But, chances are that if you're working hard enough you'll have (at least some) soreness as the result of your workouts for the rest of you lifting career.
Now, if you're still getting crippling levels of soreness even after doing the same (as in same exercise format) workout for an extended period of time, then I agree with others that something may be off in the diet/recovery areas.
That's probably a big part of the answer to your question right there. You may be on the anabolic diet, but I'd strongly suggest adding some carbs to your PWO shake. That's when your body really needs carbs (along with during the actual workout) and when it is best able to tolerate them.
I'd also strongly suggest getting at least 8 hours of sleep per night. 6-7 isn't enough for most people, especially if they're working out. I recall reading one of the authors say something like "just one night of insufficient sleep can throw off hormonal levels and lead to a decrease in performance/recovery" (paraphrased).
Might? More like probably is a big part of it. Also as far as supps, they are mostly frosting on the cake. They can and do work, but if you don't have your training, diet and recovery in order, than supplements will not give you the results they promise.
Personally, supplements that I have tried and found good results with are whey protein/recovery shakes, glutamine (actually really has helped me in the past with recovering from extremely intense workouts and is great for reducing soreness), and fish oil. I've never personally tried BCAA's, but I've heard a lot of good testimonials about them.
Once again though, get the diet and recovery (sleep) stuff in order and then if you still need additional aids, that's where supplements should come in.