The first and second raps can be easily combined with a single 60 m rope. In other words, you can pass the South Bowl anchors and go straight to Friday's Folly Ledge. This saves a little time, especially when the rap route is jammed on busy days.
Yes, I've done this many times without difficulty. However, earlier this year, the boulders in the South Bowl snagged my rope when I pulled from Friday's Folly Ledge. Thinking about it, I was quite surprised this hadn't occurred previously, as there are plentiful boulders in the South Bowl for a rope to get wrapped around and stuck on. Turns out it is a moderate, though very exposed, scramble east from Friday's Folly Ledge up to the top of Slipslide Ledge, where you can then pass through Fat Man's Frenzy back to the South Bowl.
Funny you should mention stuck ropes because I've been in that situation twice on this descent. The first time we were doing a double rappel to Friday's ledge with 45 or 50 m cords and the knot got stuck on the summit. I had to prusik back up in the dark to free them.
The second time was exactly the scenario you just described. Thank God for the Frenzy and thank Allah I'm not fat.
Needless to say, I'm no longer nonchalant about pulling ropes on this one anymore.
You should note that, to do the single 60m rappel from the summit, you need to rappel to the west, not to the south like the standard rap route. Also, no need for 2 60m ropes to do this. Just fix your single 60m and rap single strand, then have someone drop your rope as you noted.