I wondered about that problem. I had running boards on my Caravan, which uses the same sort of jacking system. It was impossible to jack it up using the normal stuff, so I modified the OE jack and found a couple of other points on each side which would work. One must be careful that the new jacking points will be strong enough to support the load and that there will be no chance of the jack slipping.
There are some promising looking points under the Odyssey, which could possibly be used, if you could fabricate an appropriate "saddle" to fit the OE jack. You could jack under the "A" frames (or whatever Honda calls the lower suspension links). The problem with that is that, when a tire is flat, there is precious little ground clearance and the jack may not fit under the suspension arm, so a higher point may be better, such as the inner mounts for the "A" frames.
All that said, I would just carry one of those small floor jacks all the time (some of them come with cases) and jack under the tiedown loops on either end of the van. I would also carry a piece of thick plywood to put under the jack, in case you have to do the job on ground of uncertain stability.
Boy, can I go on a long time and say nothing! Good luck.....
PS-You could also go to "Run Flat" tires.
Jerry O.
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2001 Odyssey GG LX