*Update: Realized this is question is a few years old - but the limitation still seems to be there and I was able to get around it with the mentioned technique. Feel free to update/correct anything here which goes against any established best practices!
While not my idea, the solution mentioned in bottom comment by "Sean Osterday" in the link below actually did end up working for my use case. I had created a New Lightning community page in the builder and wanted this page to be the default landing page.
I went to the default home page and went to add a new page assignment, from there I was able to create a new page (mimicking my already created page not sure why I had to do this as I wasn't able to reference my existing page from this menu). Once the new page was created I was able to go back into the menu and make that custom page variant I just created previously to the default homepage.
Hope this helps!