After tossing a coin I'm going with Minor 's solution. I just have to adjust it to allow for negative values (positive values mean the Home team is in front, negative means the Away team is in front). The values I'm plotting are HomeScore - AwayScore at each scoring event during a period. Or I could just shift them all into the positive.
something like this
Currently I have a separate canvas per period but they look continuous.
Edit: looking good. I decided to shift my negative data into the positive, worked well. At the moment I have a different array per period/canvas so I'm getting different scaling between graphs, so I might either switch to a single canvas or just scale the same across my arrays.
here's a WIP