We have the same essential situation (family of 4, 2 girls 9 and 13, quiet, not interested in the kids club). We sailed two years ago with them where they had to sleep on the pullout but were in an edge villa. That's probably the only thing that made it work (well that and two bathrooms). For what it's worth we are doing the same thing again this year but I really don't see it working after this year. I doubt we will do it again unless we do the PH or IS and frankly, I think we can get more out of land-based resorts when it comes to families, especially at those prices. For us, the benefits are the number of options and the multiple stops that enable a regular change of scenery without the hassle of packing up and moving to another location/resort. If we continue to cruise it will likely just be the wife and I.
I did look at the two connecting suites but then you lose out on some of the perks of an "upper" suite. Plus we love the location of the Edge Villas. Overall I just wasn't a fan of them and wish they had better options.