I believe the issue you described has to do with authentication. Even though you have checked enable anonymous access, the fact that integrated windows authentication is also checked maybe causing the problem.
My suggestion is to not uncheck integrated windows authentication, but rather create a new AppPool in IIS and use a system account as the AppPool Identity.
Here is a simple process:
1) In IIS right click on "Application Pools" and select New>Application Pool
2) Give your new AppPool a name (I usually use WorkflowAppPool) and close the form
3) Right clink on your new AppPool and select "Properties"
4) Select the "Identity" Tab> Choose "Configurable" then enter a Domain System Account and Password and then clsoe the form
5) Right click on the Virtual Directory of the Process you deployed and Choose "Properties"
6) On the "Virtual Directory" Tab, use the drop down for "Application Pool" at the bottom and choose your newly created AppPool
This should allow the webservices to invoke with a named account.