You may have good reason to have so many Arduinos so close together, but there is no evidence yet that you could not do this with one. Even if you do have multiple Arduinos, it is probably simpler to have one of them collecting and recording the data from the others on a continuous basis, thereby requiring the portable device to only ask once. This portable device need not be an Arduino. An Arduino would merely be an intermediary device, a phone would probably do a better job, and a laptop certainly would.
I understand that these "stand alone" are the slaves and the data logger is the master. Is it correct?
Not necessarily. A master merely initiates communication. After that, it doesn't matter which is which.
Unless you need to log multiple packets per second, speed doesn't doesn't merit much thought.