Reducing amount of material
Updated to match the improved question format.

There are a few ways to reduce material usage. First is what you have touched on. Which is to reduce the design by punching out holes, and removing all material that does not add anything to the structure. Even better is what you touched on, reducing it to the point where your print is more like a suspension bridge, where it is a the bare minimum scaffolding in a geometric pattern. 

Most tools you will find for reduction are like this tutorial from Shapeways on Meshlab where you reduce the surface detail. It might be worth exploring these a bet, however probably not what you really need.

Next the more hard core cad tools such as solid works will allow you to preform Parametric optimizations and Topology Optimization.
Topology Optimization. seems to be your real winner



Now from the 3d printer standpoint we just simply tweak our slicer settings. There are entries for Infill. I usually print with 7% infill. AKA my print is 93% hollow inside. I then set a few solid shell layers. Think of solid shells as the skin. Usually that is enough to reduce my plastic usage. The only reason I don't make a part 100% hollow and a few solid skin / shell layers is that I need something to print on top of or if I need the part to be strong . Even low percent infill can be very strong if the correct geometric pattern is used (I.E. triangles).

Generally the reduced infill will be enough, unless you are making thousands of this item, though in that case you are probably not going to 3d print it anyways.



3dprintingforbeginners has a nice article on the relationship between infill, number of shells and part strength. A bit more information about the terminology (infill/shells/etc...) can be found on 3D printing blog.