Here is raw, barely tested script.
Phi_multiple doesn't do anything.

Edit: Seems using the same i index 2 places in the same for loop, may be bad for a script...
Edit, changed 2nd usage of i index to a k index. Put the index start point back at zero, (like in other MoI scripts).
This got rid of the hole at the south pole.

Edit: Deleted the old script, due to poor programmer understanding of when/where to do updates to factory/factories.
Moved the factories update out of the i and j loops, and added a simple factory update. Much faster performance.
Maybe the factories is not even needed?

Could upload new version, but maybe should work on it some more...