Thanks, ChocoMom. For this batch I was more interested in fresh bananas, but those seem like possible alternatives.
Jim - I think you nailed where I went wrong. I'd seen some recipes (for fruits other than banana) that seemed to not call for bringing the temp. back up after the fruit was added, but I think it's a must. After a night in the freezer, I've brought them back up to room temp. (~73F). I was able to cut the slab, and they maintain their shape on the counter, but as soon as I pick one up, gravity goes to work.