Steve's July theory got shot all to hell this year (2014), as I recall. I went (through-hike) in August last year (2013), did not have mosquito one, and had some rain on 5 days out of 23. Four in a row (typical late summer system) just after mid-point, then one more on second to last day, August 28 or so.
What you are describing, however, is a pretty short trip. I would slide it in there maybe first week of August to optimize best weather after mosquito season.
