Thank you for the reply!
I can confirm that your suggestion works for elements. Alas, I have no luck with connectors.
I cleaned up the profile and removed the stereotypes I want to copy. Thus, I only added attributes to the toolbox, e.g.:
SysML1.3::copy(SysML1.3::copy) = Copy (SysML)
SysML1.3::requirement(SysML1.3::requirement) = Requirement (SysML)
The element, requirement, works but not the connector. Also, in the toolbox the element and connector doesn't get a fancy icon, just an icon looking like <>. Not sure what that means, but when I got the connector working with a changed name it got its proper icon.
The only solution I still got is to create a dummy stereotype, with an different name than the original, that extend the connector's stereotype. I must be doing something wrong!
I can't find any examples of adding connectors. The only ones are of elements...

Update:
I just realized that it works differently if I import it as a UML profile instead of as a MDG. I only get the connector working when importing a profile as a UML profile. When I do a MDG the connectors don't work(EA thinks it's an element) . Thus, I do something wrong when adding a connector to a Toolbox - somehow I must mark those as connectors and not elements. But what? (I still need to change the name of the stereotype to get it working)
I also get fancy icons (in the toolbox) when importing as a pure UML profile, and only default icons when importing as MDG.