Herb, could you put up some net curtains or muslin for a while, while they fledge? I sometimes use stained glass film (to help with privacy until my bushes grow up). It has no adhesive, so you can move it around and take it down as needed. Just a thought.
We had the problem with window strike in one of our upstairs bedroom windows, trees were being reflected, I stuck large photos of owls in the middle of the window, no strikes since, we don't see many cats !!!.
I've tried several things @Fire, the latest is a 'party' curtain with brightly coloured strips of foil, it reduces the hit rate but doesn't stop it. Net curtains actually improve the garden image because of the way the sun moves across so they came down pretty quick. Transfers also have a limited effect, next thing to try is the stuff they put on buses so you can see out but no-one can see in (similar to your stained glass film but just black honeycomb pattern) trouble is the babies are around for such a short time each year its really difficult to test anything.
"The trouble with having an open mind, of course, is that people will insist on coming along and trying to put things in it." Sir Terry Pratchett
Have had more bird strike with this bungalow than the house before. I have film on Windows and tried other things but all five windows and conservatory get hits. Usually blackbirds ( but mine have been adults) and woodpideon the odd house sparrow but they bounce so are ok, the saddest one was a Wren. Its even happened when I've been stood at the window so must just have thick birds here.
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I just toss seed on top of my shed during the summer and fall