With most monitors being larger, and most displays 16x9, is there a way to make the gallery (using zenpage) use more screen real estate?

Yes our standard themes are outdated but there are alternatives.
Try a third party theme like zpBase, libratus or zenji
Better yet, create your own. See: https://www.zenphoto.org/news/theming-tutorial/

> With most monitors being larger, and most displays 16x9,

You cannot count on that. In fact the screens are smaller as most people nowadays use mobile devices. As Fretzl mentioned our themes are a bit outdated and not yet responsive. But there are some good third party alternatives for the time being like multiverse, zpBootstrap, zenji or zpBase.