Well, I got the console back again this last Monday and got 4 Red Rings this time. Called support again, they were willing to repair it but when they mentioned I would have to get it back to the UPS store, I decided enough is enough. The customer service representative explained that my preferred courier was indeed supported, i.e., the one that is just a few blocks away and the same one I received the latest damaged console from, but that the Xbox support system was randomly generating labels to even out the various couriers Microsoft uses. I politely asked for a label from another courier and was told there was nothing they could do.
So this will be the last time I have issues with Red Rings. The games, accessories, etc., are heading to EB Games and the console is headed to the garbage bin. Fool me once Microsoft... but I've had enough.