I like it! Having just had that experience (mushroomed cotter) on a Raleigh Sports I'm rehabbing, I can relate. My method was to put the non-drive side arm in my bench vise and position the frame so that fork rested on my bench. That seems to support things pretty well. From there, I first knocked off the mushroomed end of the cotter with a hammer and punch, then I took out the power drill and started drilled through what was left of the cotter. Fortunately, I didn't have to drill all the way through (though I've done that in the past with particularly stubborn cotters). Once I had made little more than a divot, I went back at it with a cotter press and a steel socket. That drove the cotter remains out.

I was lucky that there was enough room to get a good solid purchase with the cotter press as I have a couple of 50s Raleigh cranksets that have the problem you describe: there's not quite enough room between the ring and the crank arm to get the press solidly in place.

Neal