Welcome Family of 6! Kudos to you for doing the math correctly! Most folks look at the 6500 lb tow rating, buy a trailer with a 6500 dry weight, and then stumble into this forum looking to improve their towing experience....I didn't even do the math when we bought our first TT, the dealer told us it would tow like a dream and we took him at his word....
You are 100% on what you can tow with a loaded vehicle. You might load the family in and head to a scale and get an actual weight...you can find drive-on scales at most recycling yards, moving companies, etc., and for $10 or so they'll let you drive on a give you a scale weight. Takes about 5 mins.
We were camping in the local state park last month and saw one of these "tent trailers". Unlike a pop-up, you don't get a sink, fridge, heater, etc, it's literally a tent that folds into a trailer. What you get for trading off the amenities is more tent with less weight. This seems like might be a good alternative to traditional tent camping.
Cascadia TentsOption B that was mentioned is get a bigger pop up, tow it with the Sequoia, and take a second vehicle for additional occupants and supplies.
