The difference between Haunted Mansion and many other soft openings is that the Haunted Mansion is just a refurb with scenes being added/changed. From an operations standpoint, there's nothing being changed that would affect Cast Members' duties or performance.
When attractions soft-open or give sneak previews, it's because they're brand new and the Cast Members need practice doing their jobs with real Guests and real loading/unloading situations. (It also gives the engineers the ability to close the attraction at-will for any problems that crop up)
Expedition Everest had sneak previews and soft openings for months because it was brand new.
Nemo, while using some parts of the old attraction, was essentially a brand new attraction. Queue layout, loading and unloading, etc were all vastly different from the previous Living Seas. (Besides, the old ride-through had been closed for so long that there probably weren't many people left who were fully trained on its operation anyway) So, the cast needed some shakedown time to ease into full operation.
That's also why I don't believe Spaceship Earth will have any sort of soft-openings, because from the CM's standpoint, nothing will have changed.
The only chance you really have of an attraction opening early from an extended refurb is literally the afternoon/evening before it's supposed to re-open. The day before it opens, cast members are brought in for a full shift just to get them back in the swing of running the attraction (and go over any minor changes to their jobs, like new control panels, new spiels, etc). Late in the day on the "refresher course" day, if the cast fully checks out, the attraction is up and running and the cast is there for the full operating day anyway, sometimes the manager in charge will say "OK, let's open it up for the last few hours." Might as well, seeing as how the attraction is running and using the power and the CMs are getting paid anyway. That's when you *might* get lucky and ride it before scheduled re-opening.
-Rob