I think the pass would be more helpful for the first half of the trip, but its always possible to have it active 2 weeks into your trip, that way you get to use it in both Osaka and Tokyo- but tickets are expensive... Hopefully you're bringing alot of extra travel money, just in case.
When I went I had the 21 day pass, and I used it alot- it's a helpful tool...
Two months? July? Sounds familiar! Bring a washcloth to wipe the sweat off yourself... the damn country is a sauna in July.