It took me a while, but I realized why all images of only one of my custom image sizes were appearing as broken links in the Visual editor and not at all in published posts.
It was Adblock, in Chrome, that was preventing the image from loading - because the file, set to a size where the width would be 300px - was named to end with '300x600.jpg'. Apparently if an image has '300x600.jpg' in its name it is considered likely an ad and Adblock won't show it.
I'm going to slightly change the size, but I feel like going forward there should be a way to avoid this.
***Perhaps using the image size name appended to the end of the file and not the dimensions.
Or at least an option to do this.
I want to automate uploading different types of images for my client and I forsee many users not knowing that adblock is preventing images from showing. I knew the images should be there and it took me hours to figure out it was adblock and not wordpress.
I think a new naming convention, or at least having the option of one, would be best going forward as the list of ad filters grows.