I'm assuming you have a traditional 3D layer in the "face" position of the text that is casting the shadow.
Duplicate your shadow-casting layer, and ensure it's shadow casting property is set to "Only", so that the layer is invisible but the shadow is not.
Then push the new layer back in Z space to the back face of the extruded text. The combination of the two shadows should now look much more consistent with the extruded text.
You can add more "in between" layers if the separation of the shadows is too visible.
Many thanks for lending a hand to my question. Your suggestion of duplicating the shadow layer and pushing in z-space certainly has a beneficial effect on the thickness of the shadow. That is fantastic. Unfortunately, it also has the side effect of looking like there's jagged multiple shadows. (See my shadow comp in the screenshot for easy viewing)
Now, in my main comp, take a look at the base of the letter 'T'. The shadow thickness is getting better and starting to match closer with the extruded letter, which is my goal, but if I kept duplicating and repositioning until the base was fixed, I'd have a mess at the end regarding duplicate shadows, i.e. with the 'X' and 'E'. What do you think?
"You can add more "in between" layers if the separation of the shadows is too visible."
I completely missed this. Apologies. I duplicated until there was about 6 layers, and lowered opacity to 50. Now it is smoother, thicker, and believable. Thank you!
Edit: Here is the updated result using Andrew's solution for anyone else that might have the same issue.
There's no doubt that my "solution" is a workaround, and has some obvious flaws if you are seeking photo-accurate results. The easy way out, I'd suggest, is to just diffuse the shadow more, so that the edges aren't visible. But if you're seeking a specific look, this might not be possible.
The next step would be to follow Rick Gerard's steps in his first post within the other thread you've linked to: create a duplicate comp of your 3D text, light and surface, generate a shadow only in this comp, then nest that comp in your main comp, allowing you to use blending modes on the new shadow layer. This will be more render intensive but more accurate as well.
And a third option - use AE CCs Cinema 4D capabilities to render your 3D text, rather than the now-obsolete ray-trace renderer.
Glad you found a solution that worked for you! I use stacked layers like this all the time for rough-and-ready 3D objects. It's not perfect, but often does the job, especially on distant or fast moving objects.
Thanks Andrew! I'm actually using Rick Gerard's outlined technique to the letter.
I've been getting back into After Effects the last couple weeks and have plenty of new areas to catch up on. I'll look into everything Cinema4D asap.
Thanks again for the tips, it means a lot. Cheers.