Thank you @Ben Gimblett and TP.
After digging deeper into this issue it appears my local environment and the azure environment was not a true apples to apples test. The app allows a user to pick images to upload and then resizes the images and sends them on to the storage container. Running locally I could select large MB image files, resize them to KB size files and send them to the storage container within a few seconds. I assumed and mistakenly thought the user selected images were being resized on the client by the upload component we are using prior to sending them to the storage container but the component is actually sending the original MB size images to the server, then resizing them on the server and then sending the resized images to the storage container. Hence why running locally was fast but running the same code in azure from my home with lousy internet upload speeds was painfully slow.
The good news is that once the files are uploaded to the app running in the app service and then sending them over to the storage container in the same DC seems to be pretty quick (not sure if we actually need to use the premium drive or not, thinking we may be able to just use the standard storage). Sorry for missing this, I feel like I should have noticed this much sooner! I really appreciate all of your help and hopefully I didn't waste too much of your time!
Thanks!