I didn't realize that your walls were closed. You could do it from the bedroom side, you just have to do a more careful patch job since you will be able to see the drywall. Insulation isn't typcially added around pipes, so it isn't something a contractor would automatically do. We chose it put insulation between all of our rooms to help reduce noise. Also, you could access the pipes from the inside of your cabinet if you cut the back of the out. The thought does make me cringe, but there again, how often does anyone get down on the floor and look at the back /inside of the cabinet?

Water hammer. The momentum of the water makes the pipes hammer and move when the valve closes, creating noise. Long term it can damage the pipes (mostly by weakening the joints). A water hammer arrestor can be attached to the line near the quick acting valve and absorb the momentum. It is just an air chamber that uses the momentum of the water to compress the air in a sealed chamber.

Best solution is to replace the (probably plastic) drain pipe with cast iron, but that is an expensive and big job. Alternatively, you can install sound insulation around the pipes (looks like regular fiberglass bats, but are designed specifically to reduce noise), which requires opening the walls. Not much else you can do, except maybe earplugs.

update: I mentioned the noise issue to him not with any blame to assign, but just with my concern that it is LOT worse than it was before, and did he have any ideas what was going on. There was the leak that I mentioned, so he came out tonight, and the problem is much lessened, even if not fully solved. Though he had routed out the pipes as well as he could before, he had not snaked them (I had asked him to do this, but it fell through the cracks. I guess he didn't have his snake with him before. I had mentioned my concern for the slow flow in the very beginning) The noised seemed to be gurgling/water turbulence at the point that it no longer flowed well, about 12" deeper in than he had been able to open up before. It is still a bit noisy but no longer like a waterfall in your face. I'm not upset that he did not notice it before, as it is really in the other room, not in the bathroom, that it hits you, so he would not have noticed. Even he was surprised, and genuinely wanted to resolve the problem. For now it is about 80% better, just with a little snaking. If I seemed offended, it is only that I would NEVER not pay a person for services rendered, and for that to be suggested sort of got my hackles up. The problem was that I just didn't *know* if my complaint was valid or not, and so I didn't know if it should be fixed before the job was "done" and paid for. Some of you in the plumbing/contracting professions may also be offended at hearing generalizations about contractors, but I have had people treat me badly. There *are* people out there who assume that the little blonde doesn't know any better, and try to push me around. Unfortunately, when it comes to plumbing, they are right. I did not expect this of my contractor, but just wanted to be knowledgeable before approaching him. (And I'd still recommend him to my grandma) :)