I'm looking to head back to Chamonix in summer 2017 to climb for two weeks. We were climbing there late June/early July of 2015, and it was a heat-wave year where snow conditions were advanced by several weeks or a month compared to normal.

I've heard anecdotes that summer 2016 was also lean, so climbing earlier in the 2016 summer than normal was better. Is this accurate?

Obviously everything for summer 2017 depends on the winter coming up. Trying to decide whether to do what we did in 2015 (~June 26 - July 7), or whether to move this up to say mid or early June. If there is a trend over the last few years then this is useful to know.
Thoughts?

Depends on what you want to climb. Pure rock routes with glacier approaches are usually climbable throughout the summer, but if you´re thinking Jorasses north face for example, than you depend more on how spring was. This year (2016) mid june and even early july, routes were still on "spring" conditions, and lots on precipitation over the massif.