Fifty-five degrees is the recommended storing temperature though I've stored eggs for two weeks in our dining room during winter (65 F) with 80% success rate of hatching. The key to storing eggs is to keep them fat end down and turn them several times a day. That's easily achieved by storing in egg cartoons with one side elevated then move the book, block of wood, etc. to under the other side of cartoon in evening then back in morning. Basically your rocking the eggs side to side slowly.
I've never used a broody but believe you'll want to get the eggs under her as soon as you can in case she breaks from it before having a clutch to sit on. I agree that you want all eggs under her set at once instead of attempting to get more eggs by staggering the hatch as she wont wait long after the first hatch before rolling unhatched eggs out of nest.
A good practice is to mark the eggs your setting with a pencil. That way when she grabs fresh eggs from other hens to add to her clutch you can easily identify them for breakfast.
Good Luck