Thank you folks, everyone, for weighing in today! I asked the same question on Twitter and someone from the style manual replied that I should refrain from using the apostrophe. The reason is that CMS considers “1960s” in my example to be an adjective, not a noun. Since my clients–university publishers–tend to use CMS style, I’m going to go along with CMS’s suggestion. This is not actually found in CMS manual; it appears to be a response discussed around the office.