Ditch the garlic press and get a rocker [1], it's so much better. Instead of putting individual cloves in the compartment and pressing together, you just press the rocker onto every clove until you've collected everything. And instead of having to dig the remaining unpressed stuff out of the compartment, you just scrape them directly into the bin. Much easier to clean, too.

There are cheaper versions on Amazon, but I believe Joseph Joseph is the original design.

[1] https://www.amazon.com/Joseph-20037-Crusher-Dishwasher-Stain...