I had a long running thread on the odyclub forums regarding my wife’s 2007 Odyssey. What we are experiencing is a bit different from your issue but I will let you know what I went through.
I purchased the van with Cooper tires that were in dire need of replacement. I decided to go with Goodyear Comfortreads. These tires are incredibly quiet but after having them installed the van had a shake at 65mph. It is not always there and not always at the same exact speed.
Took it to the tire shop and they rebalanced the tires. Each time the problem was exactly the same. Finally took it to the local Honda shop and paid for them to do a diagnostic on it. They told me the shake was due to a bad front engine and side engine mount. I replaced the mounts myself and the problem was exactly the same. So back to the Honda dealer. Paid them a second time to do a diagnostic and they told me it was the passenger side driveshaft. I then proceeded to replace this myself. Problem was still there. Went back to the Honda dealer and complained that I had paid them twice to figure it out but still had the same issue. They told me that the torque converter is most likely the cause. I complained again and another mechanic was asked to look at it. He came back and declared they were defective tires from Goodyear.
So back to the tire shop. They replaced all 4 tires (they were really great about this). But still the same problem. I then posted this on the odyclub forums and one of the members suggested a Road Force Balance. So I went back the dealer and paid them $120 for the balance. When I got it back, it was almost perfect. There was still a shake, but it was tolerable and slight. My wife then got a nail in one of the tires so back to the tire place. Under the road hazard warranty they replaced the tire. Now it is back to where it was before the Road Force Balance.
So, it is my opinion that these vans are not very tolerant when it comes to tire anomalies. Possibly the difference in the way they are manufactured or maybe it is a combination of things but I have a feeling if I put the factory Michelins on it, it would be fine. Since I posted this in those forums there has been a number of owners who complain of the same thing after replacing tires. I seen complaint from both 2nd and 3rd generation owners. Also, I contacted Honda Customer Service and they were useless. They told me that there were no reports of any systemic problem and that my local dealer would be best at dealing with it.
Now your case with the slower speeds could simply be that you have a bad tire, but I thought I would share my experiences with you.
One other point, one member said they had a shake and corrected it by using a torque wrench to tighten down the lug nuts instead of using an impact wrench. This certainly did not work for my case.