Definitely stay with the fastest group that you can hang with without completely killing yourself. Will help you hugely on the timed segments but also will get you round quicker overall. However easy you are riding, there is a fatigue cost just from time in the saddle, particularly as it’s a group event so you’ll have elevated stress/arousal, plus weather can take a toll on you. So I think trying to take it too easy between segments could be counter productive.
Whenever I’ve done these kind of events the timed segment leaderboard correlates extremely closely with overall finish time. I.e. The fastest people on the segments aren’t sandbagging the rest of the course, they’re doing the whole thing at a decent speed. That was even true on one last year where there wasn’t an official overall time, there were no chips, the timed segments were done from Strava times and were climbing segments with very little flat, and there were decent prizes on offer including a power meter for the fastest man and woman. You’d think that would be the perfect recipe for somebody to take it easy in a slower group and then go all in on those timed climbs. But every single one of the top 10 times for men came from the first group to cross the line, so either nobody fast tried that strategy (seems unlikely) or it doesn’t really work.