OP, I thought your original question was how to diversify, not whether to do it or not. You might consider a stock swap into an exchange fund. I am not all that familiar, but I believe that if you hold the exchange fund for 7 years then you avoid the capital gain tax on the original stock.
I was in the same boat as you once and someone recommended this to me. I didn't do it, because of my circumstances at the time, but it might be right for you.
I am sure others posting here are more familiar with the product/process.