When I switch eggs under a broody, I switch them when I am ready. I may toss her off the nest but normally I just reach under her and remove the old eggs, then put the new eggs in her nest. If you take her off the nest and set her on the ground she will probably just sit there for a bit then eventually either run off to eat, drink, and such or she will move back to her nest. If you put them in the nest with her on the nest you don’t even need to put them all under her. Just put them in the nest, she’ll move them under her. I hardly ever do this at night, usually in the middle of the day.
Before you put the new eggs under her mark them so you can tell at a glance which ones belong. I use a black Sharpie and make a couple of circles around the eggs, one long way, one short way, so no matter how they are laying I can see a mark. Then after the other hens have laid for the day, check under the broody and remove any eggs that don’t belong. You can toss her off the nest or just raise her up and look underneath. As long as you remove these other eggs every day you can still use them.
Some broody hens will peck you when you reach in her nest, some don’t. When they peck it might be hard enough to hurt, or it might not. You might want to wear gloves and/or long sleeves when you do that.
It is sometimes a good idea to let shipped eggs sit for a day or so to give them time to reset the air cell if it has moved during shipment. I don’t know how much those eggs coming by truck will be shaken up, a lot of that depends on how bad your roads are. It’s kind of standard to let them sit overnight pointy side down to let them settle before you start incubation.