Hi GregAngley,
After you change the logo URL, please clear the caches in your browser, and reset IE to see if the logo can be shown correctly. The issue might be caused by the cache on your computer. Besides, you can open the sub site in SharePoint Designer to see if the logo can be shown properly there.
If the issue persists, would you please open a new thread for further troubleshooting the issue?
Thanks,
Reken Liu