Here in NC I prefer fall digging and planting since it gives the plants time to get acclimated and settled. In the spring, as you know living here, we can go from nice spring weather to the swealtering summer almost overnight. That is not to say that you can't do it but that you will just have to give the plant more water over the spring and summer after it is moved. Consider moving it in late winter before spring arrives. Depending on where you live here in NC, the ground should be warmed enough and not frozen to allow it in late winter.

Since the plant has been in place for 10 years, it will probably have a huge root system. Realize that you will probably loose a lot of the roots if you don't dig far and wide, but this plant is pretty resilient--I haven't fertilized or watered mine in several years even with the drought we have experienced and it still performs well for me. The plant might sulk for a year or so after the move and dividing but it should recover once it gets reacclimated in its new spot(s).