Broody hens have been doing this for thousands of years without human help or intervention. It is possible to get a hen that does not have the correct instincts but that is really rare. I trust my broody hens to know more about being broody than I ever will. They are living animals so you cannot use words like "always" or "never", but mine seldom disappoint me. I find the more I interfere the more likely I am to be the problem.
Before a hen lays an egg she stores extra fat. A lot of that can be in a pad in the pelvic area but it can be spread about some too. That fat allows her to stay on the nest and tend the eggs instead of needing to be out looking for food or water. They do not need to be off the nest much. They will lose weight while broody, but it is fat put there for that reason. It is one of Nature's ways to protect them and allow them to hatch chicks.
I had a broody hen that left her nest twice a day, for over an hour each time. I had one that left every morning for a quick 15 minutes and that was it. I've had several that I never or very rarely saw off of the nest but I know they were coming off as they were not pooping in the nest. They all had good hatches.
If you mark the eggs you can remove any that don't belong. If you collect them every day they are fine to eat. Sometimes after the others have laid I'll raise the hen up enough to see the eggs and remove any that don't belong. Sometimes they peck you when you do that, hard enough to hurt. Some people like to wear gloves and long sleeves when they do that.
Sometimes I'll lift the hen off and set her on the coop floor. She typically sits there for a few seconds and either runs out to eat, drink, or poop or she runs back onto her nest.
I've seen a hen get her chicks out of a ten feet high hayloft. She told them to jump and they did, bounced up, and ran to her. My nests are either 2 feet or 4 feet high. After the hatch is over the broody hen has no problems getting the chicks to the coop floor. They cannot get back up to those nests so she takes them to sleep on the coop floor at night. You can put a nest on the coop floor if you wish. She might use it, she might not. I put food and water on the coop floor where the chicks can get to them and leave everything else to the broody hen.
You have a problem though. Your coop is elevated and with no ramp. Even if it had a ramp the chicks could have problems until they learn how to use it. If you consider your run predator safe you might be OK letting them sleep outside at night, she will be able to keep them warm. But what I would consider is to build a shelter on the ground where they can be locked for a few days and safely sleep at night. After she brings them off of the nest lock her and the chicks in that shelter for at least three days and two nights. After that she should take them back to that shelter every night.
There are a lot of different ways you could do this. I've tried to give you some of my thoughts on how I'd approach it. Good luck!