Okay, the above description is accurate and is working mostly. However, when trying to do this with other models, the engine does not seem to recognize LOD steps for some of my models.

I have made the following files:
Ruins_Pillar1_0.mdl
Ruins_Pillar1_1.mdl
Ruins_Pillar1_2.mdl

I set the following flag in the object's action:
my.eflags |= CLIP1;

I set the shadow LOD in the main function:
shadow_lod = 2;

I set the object's shadow:
set(my,SHADOW);

It is casting a shadow, but the shadow appears to be using LOD 0, instead of LOD 2. This results in the flickering issue. For some models, the LOD 2 is working, and they are noticeably smaller than the object. However, with other objects, like the pillar mentioned above, it is not using LOD 2 to cast shadows.

This happened actually the first time I tried to implement this solution. I'm not sure what I did to activate LOD 2 shadows, but it started working right after I changed the shadow_range to 5 (from 10). Now, however, it still works even if I switch the shadow range back to 10, but only for those objects in which it recognizes the LOD 2 model.

I will keep trying to fix this...