Dan,
I’ve updated about a dozen sites to SSL this year and I’ve been surprised at the seemingly random nature of different elements that are not updated to https.
Mostly it seems to be imaged, CSS background images in plugins, etc. Customize and visual editors didn’t seem to be the issue.
The common element was the sites were hosted on wpengine and I used the PHP script
Sometimes only a few items and the last one was generate press was clean