I have recently started using Azure CDN for a web app hosted on Azure under the "Standard" Service plan. CDn was working great and page loads dramatically decreased. For some reasons, I needed to shift the web app from Azure to a shared hosting provider and I notice that CDN is not helping much with the page speed as it used to do when the web app was hosted on Azure. Are there any changes that need to be made to make Azure CDN work with shared hosting provider?
Have you tried testing with a different CDN provider to see if you still experience the same slow speeds while using shared hosting? This could help further narrow down the issue of wether it is CDN or origin server related.
KeyCDN for example offers a variety of integration options that may be of interest.