I don't keep Icelandics myself, but know local folks who do. Our summers top out in the low One-teens, so you should be good to go heat-wise.
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I think Icelandics are the one breed that will fit all of these criteria. Otherwise, you're probably going to have to take out either "great broodies" or "well above average egg laying ability." Broody hens don't lay. If you don't want to invest in Icelandics, I would personally suggest going with a breed like Australorps which are decent foragers, fairly athletic, good broody occasionally and make good mothers when they do, and are excellent layers. Your going to have to make several compromises if you go with heritage breeds.Let's do this... take out one criteria and let's see what is out there for other options on something "close".
So... Bantam or standard breeds: Great Foragers, very athletic, Great broodies, and well above average for egg laying ability.
This is what we did when we had the Cornish for so many years. I always kept a handful of silkies just to be incubators. My Cornish never lacked in broodiness, but it was usually late June before they plopped-- and once one did the whole pen decided it was time.You might be better off keeping a few hens that go broody fairly often as your "moms", like a couple of game hens - and have the rest of them be good layers, hardy, good foragers, etc.. Then you would have a lot more choices!
If you wanted to have Leghorns as your main breed, it would be easy enough to keep a few brown egg layers as your broody mommas, you wouldn't get the eggs mixed up when hatching.
I'm thinking and been doing some talking. I think production white leg horns would fit the bill real well, and opposed to hatching my future generations I'll just buy more chicks. Those birds are easy enough and cheap enough to find...