2004 Toyota Sequoia...What can I tow?

So, assuming that we want a 4K dry, 24' long TT, what models will fit my needs?

The problem i see is in order to find a bunk floorplan in a lighter weight TT , you are going to probably have to give a little regarding the queen bed or dinette. Remember slides add weight as well. A non slide unit would be a better option as will aluminum sided TT opposed to filon sided,which adds weight (sometimes hundreds of lbs.).

Its going to be difficult to find a floorplan with bunks/dinette/queen bed in the rolling down the road weight of 5000#.
You will probably have to give up the dinette and maybe have to go with a double bed against the wall opposed to an island queen bed which besides being larger is also easier to make the bed. You will have to do some digging to find a queen island floorplan with bunks in a 4500-5000# unit, but its possible.

I would add a trans. temp gauge to prevent you from cooking your trans while ascending hills. You will also need a very good set of wide towing mirrors .

Plan to travel light, you are going to run out payload in the TV with 4 people and your stuff. Plan to run the TT relatively empty as far as carrying water. Carry just enough to flush the toilet and plan to top off the water tank once you get to where are going.

This below link shows some floorplans to give you an idea, but this is just some of what's on the market. Plan to add 1000-1500# to any dry weight figure you see.
It will depend on how much stuff you carry in the TT and at which point the TT mfg weighed their TT. There is no industry standard for weighing dry weights which makes them kind of useless.
Be aware of your rear axle rating as well as tire rating. Don't overload things in those areas.

TT floorplans with specs

I would suggest keeping the trailer under 4000 lbs dry weight and under 24' length, with a dry hitch weight less than 500 lbs. I'm surmising that your receiver will take up to 650 lbs (10% of the tow rating), but check on this to make sure because IMO this will be the biggest limiting factor. I once had a 23' TT with a stated hitch weight of 380, but this doesn't include LP, battery, water, or gear; the 30 gallon fresh water tank was up front and when full I bent a rear spring on my SUV (6000/600 rating). Moreover, you have to pay attention to your SUV's payload capacity because with 4 passengers, some gear in the back, and the weight on the hitch, you might exceed the payload rating.

That 6500# Tow Rating is a BS Marketing Ploy using a base model (no options/upgrades) with a 150# driver and 20# cargo.

Base weight is 5100#
GVWR is 6500#
MAX Payload is only 1400#

Realistically........5000# MAX Trailer