I used a Dremel tool attached to a router base to take out most of the purfling channel. I have, however, become more and more interested in the shape of the purfling as it approaches the corner, so I leave that to be done by hand.
Following a suggestion by a couple violin-making friends on Facebook, I have inserted the C-bout purfling before completing the channel from the upper or lower bouts. This is still a tough job for me, cutting the curves into the corner. Sharper tools and more patience! I did find a new use for an old tool I had -- the tool with the red and black handle is a fretting tool, used to clean old glue and such from fret channels when refretting a banjo or guitar. It is much thinner than the purfling channel, and is therefore really nice for getting wood out of the corner tips.
Things look a little rough here, with the glue still wet and the purfling proud in some places. I use the back of a ball-peen hammer to push the purfling into the groove, so when people ask how I get the purfling in, I can honestly say I hammer it in.