Disclaimer: I am not a professional bicycle mechanic. This account of my experience is intended for entertainment purposes only (woohoo!), and should not be considered the advice of a professional. In other words, I'm not responsible if you bungle the job!
That being said, let me say (as commenters RB and Giuseppe assured me), that this was not hard at all! Guys, you were right, it was probably the easiest thing I've done on this bike.
Sheldon Brown, God bless him, can sometimes make things sound much harder than they are. Based on Sheldon's guide, I was certain that I would mush the cotter pin, ruin my crank, and undo all of my good work on the Runwell. While doing the job correctly is important, it is not as hard as some internet bicycle gurus make it sound. That being said, Sheldon's word on the subject is still the standard, and it helped me a great deal.
You need only three things for this job: 1) a block of wood (I used a scrap of 1" x 8" board) cut to fit under the crank arm to support the arm when you hit the cotter pin; 2) a claw hammer (I padded mine with a small piece of rubber cut from an old tube in case I missed the pin and whacked the frame); and 3) some penetrating oil to lubricate the pin. You can also
use a piece of soft metal pipe (like copper) instead of a piece of wood, placed under the pin, but I doubt if most folks happen to have a piece of pipe in the correct length just laying about--I sure didn't. I also cut a piece of thin cardboard to protect the bottom bracket if I swung wild, but it proved unecessary.
Here's the setup:
I applied the penetrating oil liberally directly onto the pin a few days before I made the attempt, since I was a little apprehensive and wanted to give myself the best chance of success. Remove the nut and washer on the cotter to access the point where the wedge of the pin meets the flat of the crank axle inside the crank arm and apply the oil directly.
Once the oil has had a chance to work, you're ready to begin. Brace the crank arm on the wood block so that the threaded end of the cotter is pointing up, since this is the end you will strike with the hammer to drive the pin out. Needless to say (I hope), the nut and washer should be removed before you go at the pin with the hammer. With the crank arm braced and the washer and nut removed, all that's left is to whack that little bugger. Strike the pin a hard blow squarely with the hammer--imagine you're trying to drive a nail in just one whack. Grip the hammer as far away from the head as possible, like any good carpenter, since this will help deliver a more powerful blow. Here's what happened after just one strike:
I then tapped the pin gently all the way out, using a little screwdriver as a tap. And that's that. The other side was just the same; one strike and the pin was loose enough to just tap out. No damage to the cotters, the axle, the frame, or the bottom bracket in the process. In fact, unless you're some sort of hulking brute, it's unlikely that whacking the pin will do any sort of damage whatsoever. That's easy for me to say now that I've accomplished it, but this had been a point of some concern. Here are the pins after extraction; the one on the right is the damaged one that was causing my clunk (you can see the stripped threads):
Here's a bit about how cottered cranks work. The pin goes through the crank arm and that flat side gets wedged tight against the flat side of the crank axle (see below).
The flat of the pin contacting the flat of the axle is what turns the crank when you pedal, and the nut is just there to keep everything snug.
I'll say more about the mechanics of the whole operation and have some better photos when I install the new cotters in a few days (when they arrive in the mail). Hopefully that will go as smoothly as this did. I sound all confident now, but I was quite nervous when I started. Just goes to show that the things you worry about the most usually end up turning out the best (and the things you didn't think to worry about knock you on your arse).