It depends on the weather you are used to, but September is still too hot for me too. Weather wise, May and October are supposingly the best weather in Japan (very little rain, very conformatble temp). Before and after the Golden week seems to be not that crowded in TDR. May has longer day time than Oct. But Holloween in TDR seems to be very popular (I've never been to TDR in that season...), but also it sounds like a bit more crowded. Fall colors in Japan (well, it depends on where you visit) is very beautiful.
so, I guess what I am trying to say is that what is more important for you will help you decide when to go.
I personally choose late April to early May, because, 1) Airfare is usually cheaper up until later April, 2) I visit TDR before Golden week (4/29~) because the crowd is much lighter, 3) I visit my family during the Golden Week to spend time, 4) very good weather (not too cold, not hot, not humid), 5) day time is longer, 6) Visit TDR again if we really wanted after Golden week again.
This only works for me. I don't recommend anyone to visit Japan during the Golden week. Crowd would be so bad not only in TDR but any tourist -ty areas. Also, you will have hard time booking domestic transportations like airplanes and bullet trains.