Replacing a lawnmower starter rope

My mower had been running a bit funny for the past several cuts, but since it always started on the first pull, I didn't give it much thought. Tonight it started on the first pull, but the engine ran really rough until it died. I filled it with gas and tried to restart, but it would stay running. At one point, there was a large backfire and then it would even turn over. I kept pulling with the occasional fire, but clearly something was wrong!
I decided to check the air filter...it was filthy - from not being changed/cleaned for several seasons. After blowing it out with a compressor, the engine still wouldn't fire. It was about that time when the starter rope snapped. Adding insult to injury, I looked at the rope rewinder and notice rivets holding it in and quickly resigned myself to a visit to a small engine repair shop.
When I got inside, I thought "I may as well Google the repair to see if it is easier than it looks" and it turned out to be quite straightforward. You have to remove about a dozen bolts, but once you get everything off the mower, it's simple to put the starter rope back in. Thanks to the online B&S repair guide for the following instructions:

You'll need a pair of vise grips or a screw driver, some rewind rope, a long thin sharp tip flexible object (the wire from a coat hanger may work) and a lighter handy.

1. Take the pulley and start to turn it so that the rope becomes loose.

2. Remove the rope.

3. Once the pulley is all the way out, with the most tension, either use the screwdriver between the spokes of the pulley, or use the vise grips to hold the pulley in place; be careful not to place too much pressure on the vise grips, the plastic pulley may break!

4. Make sure that the hole in the pulley lines up with the hole on the rewind assembly.

5. Using the wire from the coat hanger, push the rope through the hole of the rewind and pulley. Pull the rope through the pulley and tie it off. Now use the lighter to burn the end of the rope to prevent the not from coming off.

6. Now, remove the screwdriver or vise grips, while holding on to the pulley.

7. SLOWLY let go of the pulley and the rope should feed back into the pulley as you do this.

Once I re-assembled everything (I did clean the spark plug), it fired up on the first pull and ran like a brand new mower!