Clever design, if I do say so myself…but I’m not as confident in my ability to manifest it in physical form…we shall see. Since I want to use the door of the sink cabinet as a table when eating, the top/front will ideally have no protrusions, like so:
Here’s my sketch of the mechanism. To put the door on, you put the top in place and push upward, compressing the springs and bringing the bottom catch high enough to clear the opening. Then you push it all the way flat and let the springs push it down till the bottom latch engages (bottom latch must be full width or one at each side for lateral stability). To remove door, push up on the bottom, compressing the spring and making room for the bottom catch to be pulled forward.
(By the way, if scribble makes any sense to you, you’re an engineering geek and/or mentally a bit “off”)