Hi
You're going in July which is the height of peak tourist season so it will be difficult to find somewhere that is as secluded as you like.
You could try less popular places like Matareva Beach Fales on the south coast of Upolu or FaoFao Beach Fales at Lalomanu Beach.
On Savaii there's Joelan's or Lauiula Beach Fales at Lano Beach.
There's a hotel on Savaii which we love - Vaisala Hotel at Vaisala Beach. It is beachfront, very reasonably priced, has great food and is nearly always half empty except for a few Samoan families. It's recently been renovated so there may be a few more people there but I think it could fit the bill for what you're looking for, other than it not being a fale. They do have an ensuite honeymoon "fale palagi" (western style fale) sitting right on a lovely beach with a great little verandah to watch the world go by. Dinner is caught fresh every night and you can watch the locals catch it. Wander around the village and you can immerse yourself in the culture. It's location makes it off the beaten track but if you wanted to have a look around Savaii you could hire a car for the day and use any of the accommodation I've mentioned as a base.
Hope I've given you a couple of ideas
Deb