Image gallery as a field, not a content type? Tutorials I've found seem to only cover creating Image Gallery content types. Any suggestions on how to make an image gallery as a field, rather than as a content type? 

Ideally, I'd like to have something similar to the Photoswipe responsive galleries, but with captions, and appearing inside another content type, be it an article, basic page or in this case a new content type.

Perhaps there's simply something I'm missing about embedding one content type within another?
Make a View for your gallery and put that view in a block. Then activate that block for the desired content type; putting that block in the region you want it to appear.