Aliasing the old ones by reference would allow preserving BC.
you should do it in the constructor, and for completeness also add a magic __clone method:

public function __construct(...)
{
    $this->normalizationClosures = &$this->normalizationCallbacks;
    $this->finalValidationClosures = &$this->finalValidationCallbacks;

    // ...
}
// ...
public function __clone()
{
    // Break cross-clones references but preserve them inside each one.
    unset($this->normalizationCallbacks, $this->finalValidationCallbacks);
    $this->normalizationCallbacks = $this->normalizationClosures;
    $this->finalValidationCallbacks = $this->finalValidationClosures;
    $this->normalizationClosures = &$this->normalizationCallbacks;
    $this->finalValidationClosures = &$this->finalValidationCallbacks;
}

Thanks. Referenced aliases added.

You forgot to keep the declaration above

Works without, but of course it makes sense to keep the old property declarations as well. Restored now, with deprecation notes.

Please add @ in front of trigger_error: @trigger_error(..., same below

Done.

Would it be an option to remove the normalizationCallbacks and finalValidationCallbacks properties and implementing __get() and __set() for them instead? This way we could also trigger deprecation notices when the deprecated properties are used.

Yes, using magic methods would allow allow deprecation notices and also somewhat simpler implementation (no need for __clone() tricks). It would also make the properties effectively public, which could be a problem. In addition the new properties could also probably be private, unless there's some specific reason the old ones were protected.

All of these changes look like bikeshedding to me though. I checked with Packanalyst earlier and found just one class that would need to be changed for 3.0 compatibility -- and that one uses the setter methods. A quick search is not going to find every use case, but I think using the properties directly is likely rare even in custom subclasses.

Of course, I can still make the changes if there's agreement that using __get() and __set() would be preferred.