That method wont work, that is a too large change that happens to seldom. What you want is a leap second every hour for five months to switch between standard and daylight savings time and back, with a month of constant time around each solstice. That gives you a smooth transition without perceptible discontinuities.

Seems to me the most obvious answer is to return to sundials, no?

Only works during the day? Which, come to think of it, I'm not entirely clear how humans kept time at night long ago. I'm assuming they learned roughly where some constellations were?

I challenge the idea that 10 minutes is too large of a change?

I accept that it was too many changes back when we didn't have smart phones/clocks controlling the vast majority of time pieces. Even most cars, nowadays, set themselves off of a GPS signal.

Nowadays, though? A surprising number of people flat out don't notice that the time even changed until people tell them about it.

As the other response said, though; if you look at when people were on solar time, the length of an hour just flat out wasn't constant. Such that most animals are already used to wake times changing throughout the year. It was specifically our move to a mechanical method that was constant that is causing this.

To that end, shifting to a change every month would, in many ways, be a step back towards how sundials worked with constant changes. As you say, we could go even more continuous someday. That feels like it would have slightly more complications. But by the time everything is controlled by a central computer like thing, most of them would be completely obviated.