I had my water tested and the Total Alkalinity is pretty darn high; HCO3 = 390, CaCO3 = 320. I guess I will switch to bottled water as I am guessing this is causing the harshness in my lighter, hoppy ales. Palmer recommends a range of 0 to 250 in the 'How to Brew' water chapter.
That is correct. Your mash pH's are probably no where near the desirable range. Forget the softened water. Did you test the unsoftened water? You might be able to just dilute the tap water to provide the brewing water you need. Don't go using bottled water either unless it is fairly free of minerals. You will want to go with distilled or RO water to dilute your unsoftened tap water.
I recommend using Bru'n Water to figure out your water conditions and what you should be doing with it. The other thing that may be suitable for this high alkalinity water is acidification. That will knock out the alkalinity, but you would have to use phosphoric acid to avoid flavor impacts to your beer.