We have reached the point where our answer is going to be.......The bottom line that we are driving at here is that with wireless, you just cannot predict how well.....or if.....things will work in advance before you try them out in your home.
So, it might be a good idea to understand the store's return policy in advance before you buy, in case things just don't work out.
5 GHz signals are going to have a tough time reaching more than a few rooms, so you will likely need to rely on the stronger 2.4 GHz signals for more range. Everything in wireless is a compromise.
You may find that you need more than one AirPort to get good coverage throughout your house, or to the areas where you need a good signal. You are tired of this answer, but again.....
The bottom line that we are driving at here is that with wireless, you just cannot predict how well.....or if.....things will work in advance before you try them out in your home.
But, I may be wrong. Perhaps another user will have a crystal ball that is good enough to be able to tell you how well things will work in your home before you buy. Hopefully, he will post.
My house is about half the size of yours, all on one level. It takes two AirPorts to deliver a good wireless signal everywhere in the house. I use a third AirPort, an AirPort Express out in the patio area when I want to have good coverage in the outdoor area.
If I end up having problems, is my only option to manually change channels on the 2.4GHz option on the Extreme?
Whenever you restart the AirPort Extreme, it will perform a scan to find the best available channel to use at the time. If you feel that you can guess better than the AirPort Extreme about which channel might offer better performance, then you can certainly change the channels manually to see if you can find a better one to use.
Either way, you should know that other wireless networks around you have routers that are changing their channels constantly as well, so while you might find a good channel by experimenting manually this morning, that same channel may not be the best choice this afternoon, as another router may have switched to that same channel.
So, if you have the time and patience to change things manually, there is no harm in trying that. Some users swear by this.
Most users though, will get good or better results with far less effort and time spent, if they simply restart the AirPort Extreme from time to time. Users who are in difficult wireless environments often restart their router once a day. It only takes about a minute.
Hopefully, another user who has the same model of monitor that you are looking at might see this post and offer some comments on their experience.