I am surprised that nobody has suggested that you go to an older, experienced bike fitter. It may well be that your saddle is too far forward which will put far too much weight on your hands, which often results in neck pain due to the stress of supporting yourself being channeled up your arms and shoulders to your neck and then down your spine. Going downhill only exacerbates this problem. You may be trying to fix the problem via the handlebars when the true problem is your fore-aft weight distribution on the bike that can only be fixed by moving the saddle.
Of course, if you move the saddle back then you may need to purchase a shorter stem to compensate.