I custom built a teardrop off-road trailer about a decade ago when I had more time and less kids. I think you could have one custom built either locally or in China to your size and design spec for the same or less than most of the available commercial products. It depends a lot on what type of creature comforts you want and what compromises you're okay with. If you're okay with a roof top tent style camping, you can make it a lot smaller. Even something like a Jumping Jack trailer is a pretty good option if you want a rooftop tent type concept on a trailer that's bigger than 4 people.
I really like having hard sides for a few reasons - where I live now there's bears basically everywhere, so it adds some safety, but also it's nice in bad weather either hot or really cold. The one I built did not have an indoor bathroom or kitchen though. The kitchen was outside in a rear hatch, but it did have a sink, running water, a 2 burner propane cook top and a 12v fridge/freezer on a roll out drawer plus a set of drawers and cabinets for storing stuff. Basically it was a mobile kitchen plus a hard sided tent on wheels - with a solar off-grid battery powered A/C unit to keep cool in the desert. And it carried IIRC 22 gallons of water. Bathroom was a slide out portable toilet in a side panel with a tent. Shower was just a spray head on a hose attached to the sink and outdoor shower situation. The interior was just a bed and some cabinets and the bed folded away to make a cargo area for bicycles. In many ways it was nicer experience to use than my current full size travel trailer with a slide, shower, etc because it was so simple and easy to just grab and go. Now I have to do a full re-pack every trip, dump the tanks, etc. And my current one always needs some minor issue fixed because it's built cheaply by Thor. Even at 5500lbs on tandem axles it's not realistic to take on beaches or softer terrain. It just sinks in. I've been stuck once in the Yukon territory on a fire road that got soft and had to pull a winch cable to get out.
I built mine from the ground up including the chassis and I designed it around matching track width to the 4Runner I towed with and it had matching axle bolt pattern and used the same wheels, so all the tires and spares were interchangeable anywhere. It also had the matching track width so offroad it trailed nicely behind and if the tow vechicle fit - so did the trailer. And it was about 1500lbs loaded because it was made with foam sandwich composite walls.
I think you could have one built like that with room to sleep 6 in bunks and made with 2 axles on a pre-made independent suspension axle set with a great outdoor kitchen, and a simple bathroom for in about a 16x7 foot box and keep it under 3k lbs if you make the primary box out of something like Plascore honeycomb as your base and were okay with painted interior and exterior to keep weight down. I have used Plascore to build a sailboat and they can custom build panels to order, so you or a local builder could assembly in relatively little time. It's a polypropylene honeycomb core board with fiberglass on both sides and it makes a super rigid light weight panel that could be perfect for light weight travel trailer. There are many other similar products. If I were building another one - that or a foam core composite is what I'd go with. I would also consider ground pressure and design around high floatation tires. That's easy to do if you're starting from scratch but hard to retrofit.
Anyway - long story, but you could definitely build something for 6 people that is probably better than most of what is available on the market and super off-road capable as a one-off project and keep the weight low enough that it would be easier to take into the back country. I think finding the tow vehicle that's comfortable for 6 might be just as challenging now that the Suburban has gone pretty hard toward minivan life.