TFS Online has since been replaced by Visual Studio Online and since by Visual Studio Team Services. The XAML based build engine has been marked for deprecation and will be removed from Team Services in the near future.
The hosted build controller has since been upgraded with build templates for Visual Studio 14, upgrading to the latest tfvccontinuousdeploymentTemplate.14.xaml
may also sole your issue until the XAML build engine is removed.
The new Build Engine ships with a "Deploy to IIS" task and there is a 3rd party MSDeployAllTheThings extension which makes it very easy to pick up packaged Web projects.
Your solution to switch to InRelease has since also been replaced by 2 different versions of Release Management and the latest release management feature uses the same tasks as the new build engine uses. So it's able to use the same Deploy to IIS and MSDeployAllTheThings task.
Due to the fact that this question is related to a SaaS solution, the old options are no longer available or will soon be removed.