You can do exactly what you suggest. You do not need to create a separate menu or change the php of a page template.
If you add IDs like you suggested as anchors, then your menu items can just specifically target those IDs via the # sign.
To control the link to this degree, you will need to add “Custom links” instead of just selecting the page from the list.
Example Page: (domain.com/about-us/)
Item on example page : <h2 id="history">History</h2>
Menu item: Custom link pointed to domain.com/about-us/#history