I didn't find a bathroom the whole ride where the floor was dry enough to change shorts without gymnastics, particularly at loudiac. I guess that's why people get hotel rooms. There is a school of thought that you want to ride past loudiac on the first day, so I've thought about the issue of riding past my bag. I came to the conclusion that a pair of shorts, socks, and maybe gloves would be easy enough to carry if I did that. Alternatively, showering and changing at loudiac and continuing on is an option as well. In 2011, I had severe shorts related issues on the first day, so the shower and rest at loudiac was a ride-saver for me. I changed shorts there and they worked a lot better than the ones I started in, so I just wore them the remaining 3 days. Turns out that just because a pair of shorts works well on a 200k doesn't mean they are going to work over 400k. Took me a couple more problematic rides before I started carrying a spare pair of shorts.
As Nick says, the $35 I spent on the drop bag really is nothing in comparison to the freedom it gave me. Sleeping in clean clothes is really nice