A few thoughts from a guy that works in Fusion all day every day.. Avoid working with meshes in solid modeling spaces. It's almost always avoidable and it generally doesn't work well. It should be trivial to make a parameterized Gridfinity component that you can use as your starting point. As much as you're not loving it, once you understand how to use Fusion, a tool like other tools, you will hopefully find it to be fast and powerful. I'm happy to help.
This is my approach with the Gridfinity Fusion plugin. I use the plugin to make the bin that will fit my part:
Next I draw a sketch on the top face of the bin:
In this case I imported a solid of this cutout because I've used it elsewhere. Then extrude the sketch to taste:
I like the plugin because it makes the base so quickly.
This is my parts bin with tab for a label:
This model is fully "parameterized":
When I change a parameter the model changes:
I've printed over a thousand of these in all sorts of sizes. There are limits to how small the side with the label tab can be, obviously.
The base sketch that shows parameters (fx) instead of numbers for the dimensions:
The extrude with the height:
It takes almost zero additional effort to use a configuration to control all this:
You can have as many configurations as you'd like.