1) You could have a 'segmented' cargo ship.
You have the main surface ship suitable for harsh weather as mentioned in Trish's answer. Short and tough. With all living quarters, engines, and possibly the most valuable cargo containers.
Then instead of having a traditional long cargo ship that will break apart due to shifting cargo, or due to its own weight when it loses contact with the water, you have segmented cargo hulls. Like a train, pulling cars behind it but have a ship towing floating hull barges. I wouldn't just have one tow line but several dozen. It would still be fairly rigid but allowing the length if the ship to always stay in contact with the surface water.
These floating barges would all be fully double hulled like traditional modern hulls. They would be able to maintain their own orientation ie won't tip sideways or flip over but stay 'right side' up. Not round or spherical but square or rectangular.
I would limit the number of segments, to one or two, possibly three, as otherwise you get too much sideways movement during storm activity. You can also have it, that this segmentation only occurs during storm activity. All other times the ship is pulled back together and travels in the traditional streamlined manner.
You may have to redesign the ship propeller system. Make the trust come from the forward section rather than 'rearwheel' drive.
2) I assume storm activity wouldn't be continuous? Instead of a padded room you can have safety rigging
or webbing near all system critical systems. Crew can lash themselves into the webbing that would provide a limited 'suspension' unit. They would be protected from most of the random ship movements and still be capable of work in a particular restricted area. (this isn't like being tied in place, but rather hanging in a suspended webbing similar to bungy ropes, but not that stretchy. Or you could have a combination of different rigging systems depending on what sort of work is necessary)
You may find that your storm crews will be larger than modern day earth crews, to compensate for this restricted movement during storms. Instead of one or two engineers running all over the place ensuring the engine is working, you have three or four (or more depending on engine requirements) located at all necessary critical areas in suspension webbing.
Crew sleeping quarters will probably be designed to allowing sleeping in a lashing/webbing. Recreational night visits may be very interesting.
Of course, there will be scenarios that require people to move around as needed, especially in emergencies. Ensure all machinery, furniture corners and wall edges are rounded. Ensure that everything is tied down and prevented from flying around. Essentially childproof the ship.