I suspect that the first section built was the bottom-most section, the sphere... and that section was built as a big spaceborne environment... basically, I see this as a hollow shell with an "artificial sky" and so forth. Probably built a very long time ago, during the reconstruction.
Next, the middle "mushroom cap" section was added. We know that this is a dock section, because in ST-VI we see four underside-mounted spacedoors around the rim. It's probably a smaller space-borne construction yard, capable of handling smaller-scale vessels. But for the really big stuff (1701-ish ships), it would've been way too small.
Now, in between the "yard" and the "habitat sphere" I imagine it was originally just a lot of trusswork, tankage, etc... very industrial-looking. Not the smooth, cylindrical look we eventually have in that region. And I suspect that the "yard" was cruder initially.
I suspect that "the yard" was already underway, if not already in existence, at the time of the NX-01, albeit in a much cruder (and probably nearly unrecognizable) form.
The big problem was that with larger vessels being constructed, the spaceborne facilities couldn't handle anything that big... and thus the big components had to be constructed planetside and be lifted into orbit (not all THAT big of a deal, construction-wise, but a MAJOR issue in terms of transit time... sort of like making parts of a device in China, shipping it to Akron, then shipping it to Germany, then back to Akron again... not technologically challenging, just not the most efficient route).
SO... they created another section... the Spacedock complex... on top of the existing Starbase One structure, providing an otherwise essentially unobtainable environment... microgravity combined with a breathable atmosphere, capable of holding some really BIG ships not only in segments but in fact COMPLETE.
I'm convinced. And, with a little squinting, one can see the three segments you describe as being from three different Treknological eras: (1) bottom sphere-and-post from the Daedalus era; (2) middle mushroom from the K-7 space station era; (3) flashy, well-lit top mushroom cap from the post-TMP era. I like it. Also, if we assume that Spacedock is a Federation Starfleet build, it makes sense that there would be several of these stations spaced around the Federation that were all upgraded according to the same plan.
Thanks,
--MyClone