Loved the movie, someone has actually sat down and thought about it rather than following the herd.
The gantry connects to the bed. Presumably linear blocks are screwed to the gantry, linear rails are screwed to the bed.
If you want to add dead weight to cancel out vibration, by all means bolt the gantry to the building.
Maybe I an missing something, but I don't see any need for bracing because the bed does not reference anything apart from the gantry.
Cutting steel badly indicates that it might cut aluminium alloy reasonably well