Would there be anything wrong with using eval here? (I honestly don't know -- just guessing -- and of course the following is untested):

...
   for my $test ( @tests ) {
      if($mask & $byte{$test}) { # (updated: forgot this line initiall
+y)
          eval "\$t->$test() or die";
          $mask ^= $byte{$test} if ( $@ );
      }
   }
...
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I may be wrong, but if I understand your post, I would expect something like this to do what you want while keeping "strict".