The solution was for all the shells to be spherical patches with the same radius (75.2 metres - not sure if that's internal or external).
That's what these sentences are getting at:
But now it struck him that as they were so similar, each could perhaps be derived from a single, constant form, such as the plane of a sphere.
By finding the parts of a sphere that best suited the existing shapes of the shells, each new form could be extracted.
The advantage of that is that all the shells can be built by assembling some number of identical parts. If you have a small tile whose curvature is 1 / 75.2 metres, then you can cover all of the shells with those tiles [1]. If you have a section of girder whose curvature is the same, you can support each shell on networks of those girders.
[1] Okay, so you might need two shapes of tile to cover the surface, although if you're prepared to do some trimming you can get away with one!
The most amazing thing about this story, repeatedly trumpeted to the skies, is that anyone thinks there is anything to it. "Architect discovers that standardizing the curvature of curved parts reduces expense and complication!"
Next up, spherical balls bounce straighter, and circular wheels roll smoother. Who could ever have guessed?
https://en.wikipedia.org/wiki/Peter_Rice#Sydney_Opera_House
https://www.arup.com/perspectives/traces-of-peter-rice
There's a chapter about the Sydney Opera House in his autobiography.