OK guys - job complete! Took the floor jack and a small block of wood, lifted the left side up at the frame; threw a couple jack stands under the frame (driver-side, just ahead of the muffler-cat converter interface) and went about unbolting the muffler and tailpipe from its mounts and finally from behind the cat. Once it was dropped down, fishing it out wasn't too hard, with the extra space created above the axle. I needed my wife to help guide it out from the back over the axle, while I guided the heavier muffler end out from under the driver side. To install the new muffler, I found it helpful to remove the gas tank shield first. New one went in without too much trouble. My biggest concern was to avoid scratching it up and giving corrosion an early chance to take hold again. Mission accomplished.
Ran it up and down the street and it sounds great again.
The whole project was prompted by my discovery that the heat shield on the top of the old muffler had rusted on the ends and was just laying on top of the muffler rattling every morning, until it became hot enough to settle down from expansion. When I discovered that, I also noticed that the rubber piece to the muffler mounting bracket, which stabilizes the muffler and cat to the frame, was broken. Can't tell you how many months I listened to that intermittant rattling before I finally realized it was coming from the muffler.
Anyway, it's now fixed - thanks for the help!