I am so sorry for those who have lost so many buds, or outright scapes!
I know very well what that feels like. I get hit every year, and the damage this year was extreme. (We had to go out of town at just the right (for the deer) time... With no dog to discourage them...)
I am surprised, Dennis, that you think the rabbits have been attacking your scapes. How did you come to that conclusion?
I say these things because I am plagued with both rabbits and deer. I get tons of deer damage - and it is clearly deer - to my daylilies. The rabbits run around and through the clumps of daylilies, but (except perhaps for an experimental leaf munching or two) never bothered them.
I must point out, however, that deer also
eat daylily foliage. I have one clump of daylilies, 'Bunny Eyes', which I have not seen bloom on for literally years, because the deer keep munching the foliage on that particular clump. Spray or no spray! It must be deer ambrosia! I am finally going to dig and pot it this year, and put the pot in our fenced side yard.
I am surprised about the thrashers breaking the tops of the scapes. One year I had some visiting thrashers who made a mess of scattered mulch as they (apparently) went about in search of slugs and snails. I don't think they ever broke any scapes, though. Wow.
As for leaving the scapes on, in hope of sideways branches with buds growing out from the lower bracts.... Wow, that's another thing that I had never heard of. Sometimes the deer will leave a tiny bud or two left on a scape, so I leave the scape on the plant to grow the bud(s) (every bloom is precious!), but I have never observed anything coming out of the lower bracts.
Maybe this is climate specific, or needs some particular cultural practice to encourage?