I personally think it counts as overblown "purple prose", and that your intuition that it simply means "completely" is right, although that is influenced by its (already) extended use as land-, water- and airborne. Perhaps "multifaceted" (which collocates with English "approach") might be a good equivalent.
Meaning 3 of zdic.net is generally limited to 立体战争, which is basically triphibious warfare (the translation "three-dimensional warfare" is not correct in English, and could lead to severe misunderstanding).
The link between 立体, which at root means a "raised or standing body" and the semantic field of "to do something completely via many methods" is due to its roots as a calque of the technical root "stereo-" in English and other Western European languages, derived from Ancient Greek στερεός, meaning "a solid".
Being in the 3D world, a "solid" is therefore of greater complexity than plane objects, and thus in science and technology "stereo-" came to mean various modes of perception of 3D space. One of the earliest words based on this was stereopsis, now generally referred to in English as stereoscopic vision, which has the Chinese translation 立体视觉.
In English "stereo-" is not only rather opaque to the modern reader, used primarily in technical contexts, it is also a bound morpheme. The Chinese 立体 on the other hand has taken on a life of its own, and has expanded continuously to other niches not taken by "stereo-" in English. This accounts for meanings (3) and (4) in zdic.net.
For what it's worth, this is actually the first time I've seen 立体 used with 还原, and I thought it was a technical term. I parsed it as "stereoscopic neutralisation", and I was wondering "is that even a thing?"... Am now wondering whether there is something that counts as 立体还原 in photography and optics.