"As you can see, the first two dimensions refer to the location of an object and the third refers to properties of that object such as flags and other data."

However you later state: "I don't have methods, so I don't believe I'll go the OO route."

Well, too late. You already have and now you are trying to change the rules. Instead you should store the fact that an object is on the canvas and it's location. Use an array to store this info like so:

my @widgets = (
 { object => $object, x => $x_location, y => $y_location },
 { object => $object, x => $x_location, y => $y_location },
 { object => $object, x => $x_location, y => $y_location },
);
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Note that those variables names are just placeholders for the real variables and their data. This way you only have to be concerned with the grid points that actually have data.