Glad you found that SQL screener interview question helpful and sorry if the date/time manipulation made it more complex than it needed to be :).
Regarding the visualization capabilities: I would change the shape of the events from a line to a solid bar. When you combine that with the connections (which you're already using) it will look more like a directed graph like you're interested in. End dates are optional for events, so you should be able to get by with or without it. Happy to discuss more over email: help@preceden.com. Regardless, good luck with your visualization, it's a fascinating use case.