How to avoid Dependency Injection constructor madness?

You are right that if you use the container as a Service Locator, it's more or less a glorified static factory. For lots of reasons I consider this an anti-pattern (also see this excerpt from my book).

One of the wonderful benefits of Constructor Injection is that it makes violations of the Single Responsibility Principle glaringly obvious.

When that happens, it's time to refactor to Facade Services. In short, create a new, more coarse-grained interface that hides the interaction between some or all of the fine-grained dependencies you currently require.

I don't think your class constructors should have a reference to your IOC container period. This represents an unnecessary dependency between your class and the container (the type of dependency IOC is trying to avoid!).