Mmmm, I have thoughts. I'll say them.
They've been said before.
We've been down this road with folks. A mini-van with a 3500# towing capacity. That was me a few decades ago.
First a 3500# tow capacity is generally based on two people weighing 150# a piece (if you read your owner's manual). Add an extra person and the weight of cargo/stuff in the mini-van you take camping, that limit goes down.
Second when looking at trailers you don't go by the empty weight of the trailer (the UVW or "Unloaded Vehicle Weight) because trailers salesman/data and politicians lie. Yep, it's true <shocker>. You have to go by the Gross Vehicle Weight Rating which is generally a minimum of 3000# which is the empty weight plus Cargo Carrying Capacity (GVWR=UVW+CCC). Your trailer by law should have a manufacturer's tag with the GVWR on it.
Third a trailer that pokes up taller than your vehicle is like towing a barn door down the interstate. That amount of air pressure resistance reduces your tow weight (and drops your gas mileage considerably). Some owner's manuals have a formula for calculating the impact on weight limits and some don't. But there is an impact due to towing taller than your vehicle. The fact that the leading face is curved doesn't matter.
Fourth your transmission will wear out (I had a Dodge Grand Caravan with a 3500# tow limit on a dealer installed tow package) since you would be towing so close to your weight limits. And you'll go through brake pads more frequently. Expect to pay every other year.
Fifth you can say ol' Ed is full of garbage and I'm gonna do what I want to do. And the when you're overweight and have some momentum travelling down a highway and have to stand on the brake for an emergency (somebody cuts in front of you, your light turns red, or make a fast move) and you STILL end up in the middle of intersection PRAYING folks don't hit you because you couldn't stop until you rolled 100 feet past the STOP sign/red light, you might survive and not kill your family. Anti-lock brakes won't stop you short of the intersection.
If you have to keep the Odyssey and are comfortable with a pop up they definitely have some in the 1800-2000 pound range. Which in my 100% un-professional opinion is the Odyssey's true max range.
Sixth if something happens while towing while over the weight limits and God forbid your vehicle or trailer is involved, you may have taken a chance and ignored the numbers. But the insurance adjusters from the other side's insurance company won't ignore the numbers. They've got them down cold.
Bottom line is mini-vans are good for light pop-ups (that tow below vehicle height and have GVWR less than 3500#. It definitely sounds to me like you're looking for a trailer beyond what you can tow. You should reconsider what you are looking for in a trailer IMHO or pursue a tow vehicle with a higher tow rating.
Bama Ed
PS - there are plenty of stories of people towing over-weight trailers with under-powered vehicles. It's not a question of whether you can get a towed trailer rolling. The problem is when you you have an over-weight trailer rolling and you have to get it stopped quickly/safely. You should build in a safety margin between your effective towing capacity and your GVWR of whatever you tow. I would want a 5000# stated tow capacity vehicle at least to pull a 3500# stated GVWR trailer.
on the factory installed class 3 hitch AND the transmission cooler. And of course a brake controller. If we were going to do this I was determined to at least do it right.
. Note a WDH does not give you more tow spec.
