That was actually my first idea, but I was afraid that would also confuse people since the term application is also used a lot. Maybe it's not such a bad idea after all. It would make some other things easier further down the road...

I see a difference between a domain service and an application service. If I were to put the service package in the domain, it would become a domain service. In this case, it is an application service, who has a different role and different responsibilities.

Because I don't see it as a part of the domain model, but as a facade between the UI and the domain model.