if you already have a list of the keys of the middle hash (A,B,C), then you can do this:

my @listofkeys = ('A','B','C');
@sortedlistofkeys = sort { $entry{$table}{$a}{RANK} <=> $entry{$table{
+$b}{RANK} } @listofkeys;
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Update:
Got beaten to the punch, and dragonchild had a better answer, too! ack!