I see that I can assign my "media source" - but regardless of how I set this, I can't get it to show the image file I use. Note that this is calling a custom content type, fields created with pods.
Welcome to our forum.
Can you please send me your post grid page url and if possible please send me a temporary admin access to your site, i will check how your pods working.
If no media source is working foe you, in this case you can use filter hook to override default media, Please see the documentation.