With some help of a MSFT guy, Valery, I was able to fix this problem by double checking my configs making sure that nothing is pointing to version 1.8.0.0 and I have the assemblyBinding redirect config added.
While we dont have the new version of CloudFX release with the support to Azure SDK 2.0, all you need to do is add manually in the config this redirect at runtime/assemblyBinding/
section:
<dependentAssembly>
<assemblyIdentity name="Microsoft.WindowsAzure.Diagnostics" publicKeyToken="31bf3856ad364e35" culture="neutral" />
<bindingRedirect oldVersion="0.0.0.0-2.0.0.0" newVersion="2.0.0.0" />
</dependentAssembly>
And that Azure-specific trace listener called AzureDiagnostics explicitly pointing to Microsoft.WindowsAzure.Diagnostics version=2.0.0.0
With it you should be able to use CloudFX with Azure SDK 2.0.