I was (for about 2 years) towing at least twice a week with my 91 toyota p/u. Trips were between 325 and 600 miles round trip. Let me give you a little better idea here.
I was towing s30's/s130's/z31's. All was being done on a steel 16ft car hauler with wood floor that was completely oil logged. Trailer weight in at about 1200lbs. Truck was about 3500lbs with passengers. Oh, did i mention its a 4cyl truck. We usulally weigh around 4700 comeing back out acrose the scales at the scrap metal yard. Going in was another matter. We were usually in the 6500lbs to 9500lbs range. GVWR is 4400lbs and CGVWR is 6700lbs!!!
Dont get me wrong, those "heavy" loads were hell but the ones that were at or just over the rating were no big deal. I know your van has more power and brakes than I have. The only problem was those heavy loads liked to pull weight off the front end, making the front tires like to lock up. You wont have this problem being front wheel drive and only having 350lb tonge weight.
The only thing I would be worried about in your case would be the tounge rating. I would stick with a car dolly or tow bar. If you are under or right at the manufactuers combined weight rating then your tranny should be more than willing to do its duty. ESPECIALY only a handfull of time per year. If you opt for the trailer get breaks.
All in all I say the Honda should have no problem with what ever you choose to do. Just be aware of what is required of you to tow at the vehicals limits.