Does "more recently" just mean "recently" here?
Solution 1:
Answer from comment by Fumblefingers:
more recently = later than the 1960s (in a context where there's some meaningful connection between all three of the 1960s, that later time, and now / time of utterance. Without the word more, there would be no implied reference to the 1960s, so it couldn't mean later than the 1960s - it would have to mean a little while ago / shortly before now.