Successfully replaced CR2701-04 with 1N4936RLG - no change in behavior. Not worse, not better.
For anyone else who may wonder: The diodes definitely have the legs bent under the board. I first cut the diode out close to each side of the body. Then I flowed each remaining leg and wiggled out with tweezers. Then wicked the remaining solder which left a clean via to work with. Installation was about a 4 second heat application at 600 F tip temp.
Anyway - still open to further suggestions.
