Here are some issues you may run into:
-Finding a seller that wants to move to Beaufort, SC specifically is EXTREMELY difficult if not impossible. Most sellers of homes move within the same county line let alone across the nation.
-Another issue is value, as we know home values in CA are VERY different than those in other states. A million dollar home in Los Angeles may be the equivalent of a $200,000 home in Las Vegas.
-Hypothetically speaking, if you were able to find someone willing to move to Beaufort, SC there is a chance that they may not have the same taste in home style and decor. Remember, beauty is in the eye of the beholder.
Honestly, I suggest that you list your home up for sale in SC and come down to LA and have an agent show you homes in your budget and in the city you prefer to live in(we can help with choosing this as well). This way you can make sure you find something you like before you make such a big decision in moving across the continent. You are much more likely to find a buyer for your home within South Carolina. The key would be to advertise ALL OVER South Carolina, people are much more willing to move a couple hundred miles than a few thousand miles.
By the way, off topic, but your home sounds beautiful.
Best of luck to you, hopefully it all works out, if I can be of any assistance feel free to contact me anytime.