I'm not sure if this explains all the symptoms, but could one factor be water droplets from the shower blocking and then unblocking the static port? I mean covering then uncovering the port, rather than going up it.
The aircraft might have been in a gentle climb due to a mild updraft.
This might not be noticed in the poor visibility of the intense shower.
Each time the port was covered then uncovered:
- The altimeter would freeze at a historic height, then unfreeze and suddenly show the true height.
- The VSI would slowly fall to zero, then suddenly show a large erroneous climb rate. (I think).
Having seen how an ASI needle flicks about as a bug gets pushed up the pitot, I can definitely believe the 'instant' movements.
Edited to add: it might be streams of water rather than droplets.