Thanks for the clarifications @rabbitskmc !
I’m a bit confused about the file originalimage-680×510.jpg since you don’t mention that size as either an old one or the new one.
It sounds like you removed the registered sizes and the regenerated thumbnails with the delete old images option checked. Since these image sizes were no longer registered, the files got deleted and you have broken URLs in your posts.
There are several ways you can try fixing this:
1. Edit all posts manually or using a database tool. Tools for bulk editing database entries can be dangerous if you are not sure what are you doing and may not work in all cases.
2. Register missing sizes again and re-run regenerate thumbnails. The missing sizes should get recreated and URLs won’t be broken. You can end up with a lot of files on your server by doing this. Also, you need to know which sizes need to be re-registered.
3. Try using Jetpack and its Site Accelerator feature. Jetpack creates required sizes on the fly and saves them on WordPress.com CDN (for free). The upside is that this can be a fast fix and it can reduce the number of files on your server. The downside is that removing a file from WordPress.com CDN can be difficult, ie. you need to know exact file names (with sizes) that you want to remove.
You can check out the documentation here: https://jetpack.com/support/site-accelerator/
Please note that I don’t know if any of these options would be wrong for your site since I don’t know how it was built and the site setup. In any case, I recommend you create a backup of your site before making any changes.
As for the screenshots, you can add them to a public document (Google doc for example) or use a tool such as https://app.prntscr.com
Hope this helps!