Leap minutes. You only change your clock when you have accumulated a minute of error. Then you only need to change it once per century

That actually sounds like the worst of all possible worlds!

It's infrequent enough that most systems won't bother implementing it, but a big enough time difference that it absolutely must be handled correctly at the right instant.

You'd be setting yourself up for a millennium bug-sized panic every century. And as soon as that the generation that experiences one retires, their successors will start saying "there's not going to be a leap minute for the next couple of decades, and there's no chance our code will still be running then...", and the cycle will repeat. Again and again and again.

The leap hour proposal is better because if it really is still relevant in however-many-thousand years, we can do a long-term plan to handle it which includes giving a century of notice.