OK. So as I wrote, tag(layer) order makes no difference in a 3D space. It actually doesn’t even make sense to order things by tag/layer when working in 3D space. That’s 2D thinking.
In order to make your red beams appear to go over your blue/gray geometry, you need to put some space between them. Here I’ve moved all the red elements up in the space.
So now in the top view, elements that should be below the red beams don’t show through. Compare the doors, for example.
It depends on what you need out of the model. I find the drawing tools easier to use in SketchUp but if you have no plan to utilize the 3D model space you might find it easier to just do all your work in LayOut.
Do you only need a plan view or do you also need elevations in your final product? If you need both, it would make more sense to create a 3D model in SketchUp and make the 2D views you need. That way when changes are required you only need to edit the 3D model. You don’t have to chase around trying to figure out what needs to change for each view like you would if you are making only 2D plan and elevation drawings.