At one time, the state nearest me had in essence three times zones. One region followed EST, another followed CST, and until 2006 the rest of the (mostly farm) state did not observe DST at all. Making travel plans was "interesting"...we had lots of meeting times/flights botched.
That sounds like Indiana, the state which (until around 2007) had the screwiest time zones, as you described.
My ladyfriend, before she moved to NY (where I live) in 2004, worked in Louisville, Kentucky, but also traveled to various satellite office in southern Indiana. In the summer months, things became confusing for her, her coworkers, and their patients because some of those offices were close to Louisville and an hour ahead (observing EDT) while others were further north and an hour behind. Sometimes, patients were waiting an hour for her and her coworkers to arrive.
In my recent trip to Louisville back in early July, we took the train to Indianapolis before driving to Louisville. It would have been rather confusing to have to change the clocks twice had Indy been an hour behind NY and Louisville. This also includes co-ordinating a bus schedule and a train schedule on our return trip.
Then there was the guy who had a Twilight Zone plane ticket back in 2001. He was sitting next to me on a plane going from NY to Cincy where he was changing planes for a short flight to Indy. That 45-minute flight listed 3 PM as its departure time and 2:45 PM as its arrival time in Indy because at the time Indy was an hour behind Cincy in the summer.
Back then I was chatting with an online friend who lived in New Zealand. They move their clocks like we do, but in the opposite direction because their summer months are our winter months. So, part of the year NZ was 12 hours ahead of me in NY and part of the year NZ was 14 hours ahead. But their clock-moving dates were a week or two off from ours back in 2000-2001, so in those few weeks in the spring and fall we were 13 hours apart. Pretty weird.
Now that I'm retired, I'd like DST all year round. I don't need an extra hour at 7 AM in the winter but I'd like to avoid it getting dark at 4:30 PM in the winter.