Thanks for sharing! I always find this process fascinating, what works and what doesn't.

One way to get a shortbread crust, like indywind says, is butter, but ghee (clarified butter) will also work, though with slightly different results. If neither of those is an option, solid shortening like Crisco or Spectrum's palm shortening will definitely work. Like with butter, you'd cut the solid shortening into the flour mixture using a pastry blender, two knives, or just your hands, pinching the fat into the flour until it's in pea-sized pieces. You could also cut your solid coconut oil into the flour this way (just don't use your hands because the oil will melt). Then you press the dough into the pan. It will be much drier, but it'll stick together if you have the right amount of fat cut in. This will give you a crust that has more pastry-like properties, like shortbread or pie crust.

One thing I find helpful when developing recipes is looking at a bunch of other recipes that have the kind of ingredients I want to use and kind of melding them together with guesswork. Here's a new lemon bar recipe from a food blogger I trust: Gluten-Free Lemon Bars with Almond Flour Shortbread Crust.

It uses butter in the crust, but you can sub solid coconut oil or shortening almost straight across. It also has a lemon curd topping.