I can't really comment on The Grand except that it seems like it's loaded with potential for longer trips. Heading out on my first backpacking/canyoneering trip there in April. Downsides: lack of water, pain in the ass permit system, super strenuous.
The trans-Zion trail would be fun, but not much of a wilderness experience and certainly not remote. Probably hard to make it into a week long trip too. I'd imagine something like this would be a reasonable pace:
Night 1: La Verkin Creek
Night 2: Somewhere between Hop Valley and Lava Point
Night 3: West Rim
Night 4: East Rim
Done.
But if you wanted to stick to Zion, you could always top that off with an overnighter down The Narrows or head out to the east side of the park and backpack into The Barracks. You could also break it into smaller trips doing just the best stuff. The West Rim, The Narrows, The Barracks.
Side note: didn't Bo Beck run the entire trans Zion trail in like 14 hours or something? Nuts...
Personally, if I had 7 days to kill backpacking in the southwest, I'd look further west. Escalante or Cedar Mesa. Maybe even a really massive loop of The Maze in Canyonlands. The National Parks are great, but there is more out there that is more conducive to your kind of trip and every bit as good (or better). Forgive me if you're already familiar with these areas. If you want more specific recommendations about any of them, feel free to ask.
Escalante - Quite possibly the best desert backpacking in the southwest, IMO. Lots of water, lots of deep, winding, varnished sandstone canyons. Depending on seasons, there's great choices and from the headwaters near Boulder Mountain all the way down to Lake Powell. Putting together a week long route here would be cake. There are also some good possibilities connecting Capitol Reef National Park into Escalante.
Cedar Mesa - The land of the ancients. Ruins, ruins and more ruins and mile upon mile of prime backpacking terrain. Grand Gulch alone could occupy weeks and be an excellent trip.
Maze Super Loop - I've been eyeballing this route through The Maze that would be quite the adventure and eat up the better part of a week. Start from Spanish Bottom via jet boat and then loop through all of the sections of The Maze. It would be a pretty advanced route, especially with the section through The Fins. But would be a ton of fun.