Additional Info... I checked the box this morning and roots are *just* peeking out the drain holes, but not spilling out, if that makes any difference.

Not a problem, you are in zone 9 so I would think you can dig and root prune now, I do this quite often when taking fuchsias into the greenhouse for the winter. I root prune and plant into smaller pots with quite a few of mine so they don't take up as much room on the benches. Make sure to sterilize whatever you use to prune the roots with. You should also cut the top back as well this will force new growth and this in turn will produce more flowers for you. Someone from your zone might jump in with more info for you but this forum is so slow some of us that grow Fuchsias don't check in very often. Hope this is of some help.
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It is, thanks! Seems odd that there is not more specific information on the web somewhere, but I have googled in vain. I'm sure the plant will appreciate some fresh, nutrient filled soil after living in the same dirt for two years.

What do you suggest for sterilizing the pruners with? And do I need special shears for trimming the roots?

I use secateurs (pruning shears) or sometimes scissors on the fine roots and I wipe the shears/scissors down with rubbing alcohol or dip them in water with a bit of bleach before I start and again before moving on to another plant. There is quite a bit of information out there, here's a link to the American Fuchsia Society, they have links to more Fuchsia Societies this should get you started in finding more information on these little beauties. Good luck with your Fuchsia.
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Here is a link that might be useful: AFS

Excellent, very helpful. Thanks!!