So, here's an update.
Cleaned pads, and replaced the rotor with a different model. Still a Shimano with an alloy carrier, but without the fins and laminated structure of the Dura-ace version. I cleaned the rotor with isopropyl alcohol. I bedded in the brakes as suggested, with a dozen short sharp stops at the start of my ride. The performance increased noticeably over the first 4 or 5 stops, and by the end of 12 stops it was excellent and seemingly as good as it was going to get.
The ride in to work was fairly dry and no issues at all. A bit of rain on the way home and wet roads meant a bit of noise returned on initial application of the wet brakes, but nothing that would really be bothersome.
The ride in this morning was properly wet, with water running across the road in many spots, and at times heavy rain. Observations:
1) The new rotors collect MUCH less muck from the roads, and the issue of debris snagging and rubbing on the rotors is essentially eliminated. It's gone from near-constant to only-occasional. This is a huge win. It was driving me nuts. I think the big fins on the DA rotors were collecting muck and flinging it onto the braking surface or direct into the calipers. The brakes had no chance of self clearing. It's now much better. Note to self: Save the finned rotors for the summer.
2) The squealing in the wet has been reduced, but not eliminated. Eventually, by the time I was in town, the stops were getting pretty noisy. Earlier in the ride the noise was less prevalent and would stop after a second or two as the brakes presumably warmed up and dried out. But by the end, they were fully saturated and consistently noisy (I don't have any "hard" stops in the second half of my commute to get them warm).
3) The brakes continue to work well, but the initial bite in the wet is still a bit lacking compared to my expectations. Don't get me wrong, they do stop well.