I would suggest late lunches rather than early dinners. Then u may miss the bulk of the heat rain and possibly crowds while enjoying foof and ac indoors.
Not a sure fire plan by any means. It can and does rain @ any time of day. But heat and crowds tend to build around 2ish
Hmm, everyone has their own preferences, but we've gone in late Sept the last four years and schedule pretty much all of our ADR's for 5pm dinners for a few reasons...
1) It gets you out of the heat at roughly the hottest part of the day
2) Reservations are typically easier to get at 5pm versus, say 6pm to 7pm.
3) You get the dinner menu, which can have better options (IMO) that the lunch menu
4) Some TS locations start their dinner menu at 5pm (Ohanas for example, so the food is nice and fresh and not overcooked)
5) By the time 5pm rolls around, it's the perfect time for us to take a break (we don't do afternoon breaks)
6) We would rather have a lighter lunch. If we have a ADR TS lunch, it's too much food for us at that time of the day, and we are dragging through the parks in a daze all afternoon.
Our first year we scheduled some lunch ADR's, but learned
our preference from that, and have now pretty much fully converted to dinners, and save the QS locations for lunch.
Now OP, regarding rain. Of course that's totally unpredictable, but of our 36 days of visiting WDW in late Sept, we've only had 5 1/2 days of ANY rain. The first year it was in the evening one day, the next trip it was the afternoon one day, the third trip it was a brief 1 hour DOWNPOUR one day, and a 1 hour shower on another, and last year it rained 2 1/2 days. Perhaps we've been blessed with good weather while there, but rain hasn't been a big factor. (it did impact 2013 though, as one day we pretty much had ponchos on most of the day

)
Sept is an awesome time to go. Low crowds, and we like the heat (except for those 94F days with 90%+ humidity). That get's a little too hot, but even that is manageable. Most days are 88-90 in our experience, with high humidity.
Dan