I'm the unhappy owner of a 2000 LX. The day after I bought it I noticed a shake in the steering wheel over 65 mph. It got pretty strong around 75+. Take a very careful notice to see if the shake is related to where each tire is in it's rotation relative to the other sides tire. Drive it to the point of shaking (over 70mph) around a long bend (approx 90 degrees) in the highway. If the shake gets worse or better and stays better or worse when you straighten back out then you have my same problem. Mine had something to do with where the axels were relative to each other. After a year of battling with the dealership and the regional service rep, they replaced my Firestone Affinitys with Michelin Symetrys. I told them that the tire IS NOT THE PROBLEM ! The problem has diminished but not gone away completely. I have talked with a Honda service tech "off the record" and he said that it is probably the differential. They have had many poorly machined differential components to include the bearings. The tires side wall stiffness only diminishes or enhances the bounce/shake. I'm unhappily living with my shake now. I've had several other problems with this van. Honda has now lost me because of this car. The ODY is NOT of the same quality and soundness of the rest of Honda's lineup. Good luck. Hope this shed some light on solving your problem.
PS: I didn't have time to spell check this thing.