We've towed with a 1999 Odyssey since we bought it new, and it has done a great job, but here are some conclusions I've arrived at: our trailer averages about 3200 lbs going down the road with everything in ready-for-use condition, including full tanks of propane
and fresh water. Even with the lower power of this particular vintage Ody it remains quite adequate for my use.
After our first 9000 mile cross country drive I was changing the transmission fluid and noticed a moderate color change from fresh. Nothing drastic, but enough to get me thinking. First thing I did was install a transmission oil temperature gauge, which turned out to be a great educational tool, telling me exactly what conditions caused the temp to increase, etc. A relatively inexpensive mod was to add
another transmission oil cooler to the one the Honda dealer sold me as a towing "must."
We have taken numerous trips since then, including cross-country ones. I change transmission fluid twice a year and monitor the color and smell closely. A week ago I changed it again for the first time since our last cross-country trip, and the color was nice and pink, with no visible contamination. Even struggling our way out of Death Valley in the heat had apparently not overheated the fluid.
Since this issue is often the main drive train weak point in so many types of drive trains I remain vigilant about what goes on and drive accordingly.
That said, the Ody is a delight to pull a trailer with. I use rear airbags to level the car (and headlights), and the tongue weight remains well under the 350lb limit. Since the airbags use an on-board air compressor I have found this setup to have unexpected benefits in leveling the rig in campsites and a decided benefit in making handling very secure. The 118" wheelbase is a feature which makes stability extremely good.
I would not try to push the weight limit beyond what I'm currently doing, so modifications and additions to the trailer are often conditional on achieving weight reductions in other things. I find it fairly irrelevant to go by the factory weight quotes since the optional equipment usually does a number on the final total. In Oregon the wayside weigh stations are usually on and often deserted, so we have the advantage of always being able to update the actual weight. It's the "only way to tow." (Reinhold, I'd consider the 17' Burro to likely be between 2800 and 3200 lbs rolling down the road.)
I agree that the Oliver is pushing it beyond what is reasonable and mechanically safe; go for a tow vehicle about 5000 lbs for that one. If you use an Ody, most of the other 17' trailers will work well.