the best time for your area would be similar for mine. if you are digging and relocating plants, it would be in late fall or early winter when temps are above freezing. container grown plants can be transplanted any time of the year but i personally would also plant those in fall or winter because of the lower temps and more abundant rainfall.
do not plant too deeply, keeping the rootball about 1" above the surrounding ground level. it will settle over time with watering. mulch after planting. pine needles or bark are popular here.

I have a similar problem here in 7a. I need to move a kumasaka that I planted 3 years ago to the front of the house as part of a re-landscaping project. Would October be a good time to move? I haven't noticed any buds on the shrub yet and I wonder if I should move it before or after the buds set. Frankly I don't care if I get any blooms next spring but I don't want to stress out the plant too much. Any ideas?

Sure, Kumasaka should flower much later than October but if you want to move it "now", October is a good time to plant and transplant. Do remember to keep it well watered if this Fall & Winter are dry.

When planting acid loving plants as these, Azaleas and Rhododendrons it is best to dig the hole(s) twice as wide as the root ball and six inches deeper then when placing the plant an inch above ground level. Adding peat moss below and to the sides of each plant gives the acidic mulch that insures normal growth. I learned this while working on a gardening crew at an exclusive performing arts center and following earning a horticulture degree while gaining work experience at the college.