I can confirm that all issues related to multivolume will be resolved if you load your time sequence as a “Volume sequence” (and not as a “Multivolume”).
To register 3D images within a 4D sequence to each other, you can use SequenceRegistration extension (it uses Elastix internally).
If you have trouble registering 3D volumes using Elastix then make sure they are cropped to the same region (no more than 1-2cm difference), have a reasonable initial pose (no more than 1cm and 5 degrees misalignment), and use the default registration preset. If this works you can go back and try gradually relaxing these conditions.
You can also try the recently added SlicerANTs extension. It seems to be similarly robust as Elastix and it exposes some parameter editing in the module’s graphical user interface.