Re: What happened to 'time travel at will'/slingshotting?
The surprising thing about it is the apparent low priority of the 1960s mission. The heroes aren't explicitly about to do anything comparable to their other time travel hijinks - no saving the universe, no saving the Earth, even. There should be a thousand time travel sorties more pressing than that. So the implication is that Starfleet is sending thousands of time travelers to do things ranging from the fantastic all the way down to this ho-hum observation mission. Which makes secrecy unlikely, and any uniqueness of the Enterprise or its heroes in time travel ability implausible.
The other possibility is that The Enterprise trip was the first attempt at a sanctioned starfleet time travel mission, and they chose a simple observation mission to see how it would work. The fact that it got complicated may have convinced Starfleet not to try again.
"What are you going to do?"
"I don't know. I'm making this up as I go."