I too have this problem with my 04 sienna. I had a Hidden Hitch class III hitch (larger than Toyota installs) installed by a hitch company. A lot cheaper than Toyota - parts and labor less than $200.
I bought the Sienna over the Odyssey because of its advertised highest clearance of mini vans. (8 in. i believe). I am not sure where they are measuring that from. I hit all the time. I tow a pop up camper (~ 3000lbs). When all is hooked up and loaded, I probably only have a 2 in. clearance. It does tow and handle very nicely though. Took a trip last fall from Maryland to Disney in Florida.
I have been trying to talk with companies about options - air shocks, etc. I have not gotten any solution yet. Toyota tells me if I do anything down that route, I may void my warranty. I even paid for an extended warranty.
So if any one has any ideas.....