Good for you anyway! There's always something new to learn with each processing session that will make the next one go faster & easier. You've set the bar at 3 hours per bird, I bet you'll beat that time by a good amount the next time you butcher chickens!
In case you haven't seen these, here are 2 good sites I like,
http://www.HowToButcherAChicken.com and
The first one has lots of great information on all aspects of butchering, you'll especially want to check the part titled How to Properly Scald a Chicken or click here:
http://thedeliberateagrarian.blogspot.com/2009/02/how-to-properly-scald-chicken-my-never.html Once you learn how to get a good scald then plucking should be as easy as cleaning the lint trap of your clothes dryer. The other link shows a great video on skinning & cleaning out a chicken. Even if you decide to pluck you can use their technique for cleaning out the bird.
It takes some experience to find your best technique for the dispatch. I think your bird was really dead if his neck was broken and his throat was cut, but they have a lot of post-mortem reflexes that keep them moving long after they've Crossed The Road. There's been a lot of discussion here about what is the best, most effective, & humane dispatch methods. You can read the discussions & decide for yourself.
I slit the throats of my birds, I use a very sharp knife & know just where to cut (behind the jaw in the bare-skinned part) to get a good bleed. You can use many different kinds of materials to make cones, they're just handy for holding the birds so their wings don't flap & their heads stay down as they bleed out. You can also bind the wings with duct tape and hang them from their tied-together legs (zip-ties or twine).
You'll get better at cleaning out the carcasses too, it's just a matter of practice & experience. Sounds like you're on the right track, just make an opening at the top of the cavity & stick your hand in there & scooch all the stuff down & out. It's not connected to the body by much, you can easily loosen everything with your fingers to pull it out. The lungs may take a bit more effort & that too can be scraped away from the ribs with your fingers.
Many folks will withdraw feed from their candidates 12-18 hours before butchering, it makes for less contents in the crop & the intestines to deal with.
Keep up the good work, let us know how much better things go with your next chickens!