Thanks again for all the advice. We reinforced the run and put in new vents in the coop so we can lock it down every night. We also installed a motion sensor light out back. Our new rooster, Big Nasty, has taken ownership of all his girls, but he especially loves the two who are laying. He makes sure they all get the bits of fruit, oats and other treats we bring out from time to time before he has any. Quite impressive, really. He gets everybody in the coop before dusk and he's quite vocal when he feels any of his girls are stressed, such as when we're trying to catch the littlest ones to put them on a high roost at night. They're not quite able to get up high on their own yet, although they're getting better. We removed any low roosts as part of our protection strategy.
So far so good. None of the little traps we set up (just piles of junk that would be moved if anything tried to get to the coop, not real traps) have been tripped, so I'm thinking the light out back has been the biggest deterrent. Either way, everybody seems safe and content. The girls aren't fighting and we're getting eggs every day from the two mature birds.
If only I could teach my big cat Mister Handsome to be a fighter instead of a lover we'd have all bases covered.......