On a hunch I changed:

for ( keys %items ) {
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To:

for ( sort { $items{ $b }{ v } <=> $items{ $a }{ v } } keys %items ) {
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Which produced a nice speed-up compared to the default hash order.

Note that the converse of:

for ( sort { $items{ $a }{ v } <=> $items{ $b }{ v } } keys %items ) {
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Was a lot slower than the default hash order.