I had the same worries - I ordered the 7-seater, then saw all of these complaints about it and wondered if I should have gotten the 6-seater. I'm happy with the 7-seater, however. A few thoughts:
1) I think that the issue with the middle seat headrest is WAY overblown. When I'm backing out of spots, I use the rearview camera. When I'm driving, I use the rearview mirror. If there is another car behind me while driving, it is very easy to see with the rearview mirror. The only time the headrest might block a car behind you is if it is wayyyyy behind you (and looks very small). But that wouldn't really impact me when changing lanes or anything. If the car is close enough to you to be an issue, it is clearly visible. I thought that this would be a real problem for me, and it has turned out to be a non-event. I think that even if you had a 6-seater, if you had 2 people regularly sitting in the third row, this would block the view a bit anyway.
2) I am a 5'6" pregnant woman and I sat in the third row and found it to be very comfortable. I didn't expect it to be as comfortable as the second row, however. The third row in an SUV is never that comfortable! But I thought it was as comfortable, if not more so, than the seats in my previous Toyota Highlander/Acura MDX/Honda Pilots. If you tend to feel claustrophobic, I don't think you'd like any of the third rows in these cars. I think that kids are much less finicky with this stuff. If you have some older sons that may grow to be 6'3" in a few years, maybe it isn't the best seat for them, but if your kids are younger/female/shorter, then I think they would probably like it back there. I'm not sure about the carsickness - I tend to get carsick wherever I'm sitting if I'm not driving, although it's not as bad when I sit in the front passenger seat.
3) A complaint about the 7-seat middle row with kids - the only cupholders for the second row are the ones that pop out of the center console. So that's 2 cupholders for 3 kids, and the cupholder popping out will take away legroom from the person sitting in the middle seat. My old SUV had cupholders on the doors so had 4 cupholders for the second row seat but you obviously can't do that with the falcon wing doors, so you lose two cupholders in the Model X.
4) How often are you actually traveling with all 6 people in you family? If you're traveling all the time with 6 people, and don't have large car seats blocking access to the middle aisle from the falcon wing doors, then it would probably be faster for people to get in and out with a 6-seater. But most families aren't always traveling with all of the kids - maybe 4 kids and 1 parent regularly, or even just a couple of kids and 1 parent. In that scenario, I think it is faster and easier to have 1 parent in the driver's seat, and then the 4 kids in the passenger seat and second row (if one of your kids is old enough for the passenger seat) - and then you don't even have to worry about accessing the third row. And you can keep it folded down to help with visibility and allow for more storage if your kids have a lot of sports equipment and stuff. Then you can just use one of the third row seats if all of you are using the car, but for most trips on a day-to-day basis, the kids + 1 parent could fit in the first two rows.
5) If you're not using the third row regularly, you can then push the second row seats all the way back and get more legroom in the second row for people. There is a LOT of legroom in the second row when the seats are pushed all the way back.
6) I can't speak from experience, but I think it would really annoy me to not have armrests on the middle row seats in the 6-seater.
7) I don't have a dog right now because he passed away in October - but I do think that the 6-seater would have been nicer for us if we still had our dog, because then he could lie down in the little aisle between the seats without taking up space in the back of the car (and without getting his paws all over the white seats!)
Overall, I think each one has its advantages and disadvantages. I'm happy with the 7-seater, but our family situation is different than yours.