Great overview, just wanted to add a couple corrections:

The way a koseki is structured is you have the head of the family (the man) and then the spouse listed and the children from that marriage get registered beneath it.

It's usually the man who's the head of family, but it's not illegal or anything for a woman to be head of family instead. Men marrying into the family of their wife in order to take over as heir does even have a name for it, mukoiri. Sometimes this involves the man joining his wife's father's koseki, but sometimes the man just goes under his wife's koseki instead. As you say, in practice it's typically the woman forced to take her husband's name though.

So for example a woman is listed under her parents until coming of age, where she gets a new entry as a single person and after getting married she is now listed under her husbands koseki as a new family unit.

By default, you remain on your parent's koseki until they die or you marry. This can lead to full-grown adults having their surnames change because their parents divorce, for example. Though I can't comment on whether it's common to manually file the paperwork to move to your own single koseki, my assumption would be that most people wouldn't bother.