The second option can be hosted at ArcGIS Online without you doing anything (i.e. loading anything). It is a REST API. Yes, it is hidden in their stupid docs.
The third option is faster than anything else, but would require you to load planet-osm.
Mapnificent [0] seems to do something similar and I had some fun playing around with it for my city. It doesn't seem to go into as much detail as Mapzen and doesn't have an API, but it's open source.
I am super sad to see this go and still haven't seen any alternative.
Happy to hear about anything in this direction :s.