I would think going with taller towers is your only option that doesn't involve moving or replacing the cooler (which you obviously don't want to do) BTW, what's your frame set up, 3, 4 bay? If 4 you might be able to put it under passengers and move the deck back... DRE and AAA will make their towers any height. Go big and cut them down a little at a time until your happy. I made new towers that used an NRS lopro to mount to the frame rail that started at about 11" above the rubber following a new boat purchase. Over the past few months of tinkering moving and learning how the boat loads down I've dropped everything almost 3" and am damn near back at the 8" towers these new ones replaced. What I found is that when you're that high off the water a little change in height translates to a big change in range of motion of the oar, so you might not need to go all the way to 13"...
As far as disadvantages, there are plenty, you hit the most serious potentially, but also there will be more leverage on your mounting system so things could twist or break more easily. The other big one is I found it strange sitting that high. I had nice visibility but I felt exposed, not just to water but to wind, cold, etc. I longed to be tucked into my little hole in the middle of the boat. Now that things are lower I'm getting used to the position and have come to like it, but I don't think I'd want to be as high as your talking about. That said, I'm sure you'll get used to it if your cooler needs to be in the rowers position. A potential advantage is my dogs could walk under the oar with out getting in my way of rowing. I thought that was nice.
Yesterday's gone on down the river and you can't get it back. - Agustus McCrae