It's strange that a late model Whirlpool wouldn't provide satisfactory results, but since it's history, there is one thing you should know about using a vintage dishwasher: You will likely need to augment your modern day dishwasher detergent with an additive that contains phosphate, such as STPP, or use an industrial detergent like Cascade Fryer Boil-Out.
This is because modern detergents are designed for super long cycles like your Whirlpool used. Older machines run relatively short cycles that, depending on the selected option, can complete in less than an hour. Modern detergents need more time to work, and if you use them with a vintage machine, you may not be happy with the results.
The KDS-19 doesn't offer a heated drying cycle, so keep that in mind if you find yourself having to hand-dry some items or notice water remaining in cup bottoms.