Do seriously consider
trip insurance though. June through Nov is hurricane season, so I would recommend checking out insurance and making an informed decision.
Equally important is knowing the canel policy on the reservation you make. I find that if I can get 24cencel poliicies that is often good enough for me.
In the past, US has been rather quiet in Sept. WDW, other than the TS dining places, is quiet in Sept - but US has been even quieter.
Perhaps not so much with the new HP. I think that will still be quite a draw, so the parks will probably be busier than before.
I think it may well be worth every penny to stay onsite at US for the extra perks. They also have deal if you are staying more than a certain number of days youget a discount.
The rest of the Time you could stay offsite over by WDW.
I'm not big on renting houses while in Orlando. So I can't help you there. (That would be my presumption when you say private pool)
The closest I coud suggest is maybe one of the DIsney mods - or perhaps another offsite place that has more thanone pool (a feature pool and a 'quiet' pool.) The quiet pools tend to be empty - and though not technically private - they might feel a bit that way. CBR and POR (Magnolia side!) come to mind as having quiet, 'quiet' pools. Being far away from the main building will give you more qiet.
The other trick to going that time of year is the often daily thunderstorms. They don't last all day, but it can really come down and thunder for a bit. You have to prep for it every day in your attire. Something like
Crocs on your feet really comes in handy - over shoes that don't tolerate water well (sneakers, some flip flops). Also, wearing lightweight clothing - just not the kind that turns see-through when wet.
Be aware too, that Septmeber is
free dining promo time at WDW. The TS places will get booked up, but QS and offsite should be fine. Indeed, if you are staying offsite, a good deal and good bet, might be to eat some meals offsite.
The difficutly I find sometimes with staying offsite, and especially with having a kitchen and a large group, is that it's more difficult to motivate everyone to get upand out. Some folks prefer to hang out at their resort, but I like to be on the go more. I can hang a little at WDW resorts, but I'm not one to sit in the room watching tv. I feel like I can do that at home for free- why spend $$$ to come to Orlando if I'm watching tv?
And last, while most kids are in school, there ARE also plenty of fmailies that show up for free dining. The parks are not particularly crowded over all, but every year there are a number of posts by folks who are surprised to see any kids at WDW. Every day of every year there are kids at WDW. Not sayig you'd be oe fo the ose folks, but at least one post here might givn the impression that there aren't many kids in WDW in September, not so.