I found what, I hope, has turned into an instant, quick, and easy fix for this problem, even to the point that it revealed the already-logged 255.255.255.255 IP addresses in their proper form. Perhaps this will be useful to some out there.
In your databases, check the wp_bas_visitors table’s visit_ip field. In my database, this field was unsigned. I simply changed this attribute, setting it to the blank item in the drop-down. Hey presto! This instantly revealed the masked IPs and, up until this point–maybe a half hour later–the 255.255.255.255s have not returned.
Now, let’s hope that this didn’t open up a whole new can of worms, eh? ??