Is using myjson.com trustworthy? Do their URLs stay indefinitely? (longevity/permanant) I realize it may not be ideal to host it elsehwere but my personal site is a Wordpress site and I don't think I can mix a custom page into it. I suppose I could look to create a subdomain and point it to it.
You can have your JSON file anywhere where it can be accessed publicly. Make sure uploading it doesn't change the mime type from application/json. I host mine on Github pages, though you may want to keep it private so your video links aren't public.
Since the file needs to be publicly available (not password protected), you may want to create a robots.txt file for the folder it is in. Just create a text file, put it one step above the containing folder, and put the following text in.