Awesome! Thank you for the great reply, it's the only time I've heard it articulated as to why busting their broodiness is so necessary.
I will look into finding eggs locally but it might take me a day or so and she's already been sitting three... Will that mess her timing up?
Also, should I go ahead and move her nest into a separate area from the other hens when I try and swap out the eggs?
The hen should be fine to brood for 4 weeks without any concerns or even up to 6 if special attention is paid to protect her health.
Moving the hen depends on her ability to protect her nest and the attitude of the flock mates. Some of my hens do great when just left in the coop for their brood, others are more timid and I do move them to isolated areas before giving them eggs.
At a minimum you will want to block off her nest from the others the last few days of incubation to give the chicks the best chance of undisturbed hatching.
A simple chicken wire cage can be used to block off a nesting area, but it will need a smaller mesh wire to protect chicks since many can fit through standard chicken wire.
I usually move a hen with new chicks to a private area for at least a few days before letting them back into the flock coop in a floor box...but I prefer the hen raise the chicks in a flock environment and over the years I have developed a very broody oriented and chick friendly flock, every group of birds is different so careful supervision and observation is needed to make sure there are no problem flock members who might harm the new additions.
Some people separate the broody and chicks completely from the flock until the broody weans them and they are then integrated back into the flock as adolescents. I prefer the hen do it and chicks raised in the flock by a broody are regular flock members (though low ranking) when the hen weans them.
If you choose to move the hen for her incubation period I would do it before giving her the good hatching eggs...prepare a private area of your choice, it should be rather quiet and dim, away from major coop traffic if possible and well ventilated and out of direct sunlight through windows or doors...
Deep, soft bedding with a slight bowl shape is good and give her a few 'throw away eggs' in it. Move her at night with minimal light and use a sheet or towel to keep her area dim for the morning after the move. If you can put a moveable pan in her current nest area now when she is out for her daily drink that would make it even easier because you could move her nest pan and all to the new area, allow her to get used to her new area and then remove the pan if needed, or let her brood in it if it is big enough. We use many moveable boxes for egging boxes, when a hen goes broody in one we just pick up box and all and move it if needed.
Mark her eggs with a circle around the middle (we use a black sharpie so it doesn't rub off) and a number. The number allows you to track any questionable egg if you think one is bad on candling...if you aren't sure you can note the number and recheck it a few days later. I usually candle on day 10 to pull clears and day 17 or 18 to pull sloshy eggs or quitters, sometimes I don't bother with a second candling, everyone has their preferences...
The more you plan now, and research and organize for 'what if' scenarios the more relaxed you will feel...the hen does the work but we do the worrying, lol.