Thanks for that explanation. The float test doesn't tell you if the egg is safe to use or not, just how much moisture has evaporated from the egg so it's an indication of how old it is.
The float test will compromise the bloom. Any egg that has been wet should be refrigerated.
Some people write the date the egg was laid on the egg so they always know how old it is. Instead of storing them in the basket you might develop a system of storing them in egg cartons and stacking the cartons in a way that you know which are oldest. Off the top of my head I can't think of another way to keep track.