Going out just to get the rain is perfect.
Waiting for some non-thunderstorm rain to show up on a forecast around here. We're in a bit of a drought, so we need it!
You're right about July and August, but the rest of the time ...
I was in Olympia for a year in the 70's and never dried out. That December SeaTac Airport officially had 15 hours of sunshine -- all in 2 perfect days. Rest of the month, totally socked in and drizzling.
Would be considerably more challenging if you were trying to do this in San Francisco or Los Angeles, where there's a fairly good chance the next measurable rain will be in October (or even November).
I personally feel like in most places rain isn't really the worst weather in the summer. Rain on a cold November day is no fun at all, but in June I'd take rain over really hot and humid.
You could have run in hail here in suburban DC last week ... (ouch).
I love these challenges. They really are motivating! I'm enjoying it vicariously.