Trook, I don't think you have any serious problems here.
Five-foot growth is pretty darn substantial stuff for any 5' cutter/tractor combo to handle. The first run through such a patch isn't going to be picture pretty and I'd expect a lot of neatening subsequently. Also understand running the cutter a few notches higher through it on the first run........done the same thing...........knock it down to something manageable first without being too hard on equipment and then go back on later cuts to make it neat.
Your R-4s are definitely wider than regular ag tires and are laying more material down in front of the cutter than R-1s would but it's all in the nature of the beast. Besides, hasn't the Southeast gotten quite a bit of moisture this Spring? If you're material is wetter and greener then it will be more likely to resist cutting since it's moist and maleable.
Lastly, there's nothing wrong with your shredder. If you want to change the blades on it, fine. Did the same on my riding mower. I've actively used 5 different brands of cutters.....Mohawk, Corsicana, Howse, Bush Hog, and Dale Phillips........and have rarely found a noticeable difference in the way they cut a piece of ground. The way I had the machine set and the condition of the blades was always the primary culprit in any trouble I had versus brand or deck design or whatever. Others on here say they see a difference, okay, that's their experience and I can't quibble with it. I don't see it to any real extent.