Why is my Azure SQL Server so slow?
For what is worth, I ended changing the VM in Azure from type A to type D and then attaching another disk and moving the TEMPDB to that disk. So my final VM now is a D2 Standard with 7 GB RAM and three data disks, one for the MDF files, another one for LDF files and the new TEMPDB disk.

I gave up trying to understand with the A3 some things you mentioned and simply upgrade the virtual machine. I even went from A2 to A3 and even though I did find some improvements, I ended up changing to a D2 VM.

In the document that you stated, Microsoft recommends a D3 for Enterprise Edition or D2 for Web or Standard Edition, and use of Premium Storage, among other things in the check list at the beginning of the document.