Don't go with too big a pot at one time, you run the risk of root rot or imbalanced watering.

It's safe to go to 12 inches diameter and use a fast draining mix, during repot, that will give you 30% more volume of soil, wash out old mix a bit and untangle the old circling roots. Make sure your nice looking pots has lots of drainage holes.

Thanks for the reply yellowthumb. :)

They are blooming right now. The three Nuccio's still have plenty of unopened buds. The Carter's Sunburst is almost done opening all its buds. Should I repot now, or wait till they are done blooming?

You should repot right after most of the flower buds are open, but right before the new growth.

For the sake of the tree, remove the flowers once they are open for a couple of days, this is to conserve energy. Hold on the fertilizer for now, fertilize slightly using an acid loving fert after flowering. Don't use too much. Once the new leaves are burnt, it will take two years for it to drop. Camellia only has two growth spurts each year.

After repot, put it into a shady location, make sure the humidity is high enough, not to stress the roots. This is the critical stage, Camellias can lose lots of leaves once stressed, that will take several years to grow back.