Update time!
I fixed all (I think) of the bugs and unresolved issues with the beam modifiers, so now they can all be selected, rotated and moved to unoccupied floor tiles. You can't move a piece to a floor tile that is already occupied. I also moved the colours for beams etc. into global variables so I can easily change the colour scheme for different levels.
Next job is to make actual puzzle levels with these pieces.
Here's a video: