Yes, I tried composer earlier today, but it did not work. The only version of the Widgets module it has is the one compatible with SilverStripe 3.1 (a beta release) so of course it refused to install on 3.0.5.
Is it permissible to roll my eyes at this point? :-D :-/
The versions of the Blog module and the Widgets module are the same as yours (thanks for that) and I'm still on the default "Simple" theme since I am still trying things out.
I don't mind "fiddling around" with stuff, but I am a little frustrated here with what seems a standard install of SilverStripe.
I know it's not your responsibility of course katja, thanks for taking the time to reply to me with some useful info, I'll have another dig around inside SilverStripe later to try to see what's going on.