To summarize this post: I don’t see Qubes OS ever being able to use GNOME Shell directly unless
something major changes on the GNOME side. The best that could be done is to ship a fork of GNOME Shell with a large number of (likely quite intrusive and non-upstreamable) patches. This means that users would be stuck with a single GNOME Shell version for an entire Qubes release even if they are using a GUI qube, and that the Qubes team would need to ship a separate package containing both GNOME Shell and any dependencies that needed to be bundled. Using an extension would not help because extensions are also patches to GNOME Shell. The only difference is that they are applied at runtime (via JavaScript) rather than at compile-time.
I think @ninavizz’s suggestion of improving KDE is a much more realistic option. UX improvements will benefit all users of KDE, not just Qubes users, and as such are much more likely to be accepted upstream. KDE is much less opinionated than GNOME, which means that it can be made to fit Qubes OS much more easily. In fact, I believe Qubes OS currently does not need to patch KDE at all.