Thanks fellas for the excellent feedback, this is all very helpful. For what it's worth, this model is a late '03 manufacture date, sold as a 2004. I know this because the Carfax shows the first registration date as being in 12/2003. Sounds like if the Honda is really that much better a minivan (condition-wise, how it drives, etc.) than the others in this age / price range that it still might be a worthwhile buy, despite potentially having to put a fair bit of money into it at some point.
My belief (and experience) is that with most imports / domestics I should get 200k or so before a major expense like an automatic transmission replacement. Sounds like I may not have that luxury with a 2nd gen. Odyssey. But there's no doubt in my mind that this van has another 5-6 years of life in it (no corrosion issues here in Colorado, vehicles will last forever if you care for them). All the major service has been done (timing belt, motor mounts, water pump, etc.) recently which should take us a lot of trouble-free miles with no worries other than the unknowns with the transmission.
So the way it's starting to appear is that I might be rolling the dice with the Odyssey in that a huge repair bill will come sooner than later. But the harsh reality is than an auto trans. will likely fail at some point during my ownership regardless of what brand I buy, as we plan on driving whatever we buy to 200k (or beyond) as long as it stays reliable.
Base models are all but out (unless we found a screaming deal on something very low mileage). We want something with a premium feel (the Sedona EXs fit that bill, but barely) like a Town & Country, or higher equipped models. We looked at the Toyota Sienna, but they're too cookie-cutter IMO-- I'm just not a fan of Toyotas of any model, they're too plain and unexciting.
Keep the input / experiences / suggestions coming! Much appreciated.