Of course crabs can be farm raised. I am not in this field but explored it in 1982 when the U of California reported success at its Bodaga Bay research station with lobster farming, they were using pelletized grain and had to add a sterol compound only found in fish or else the lobster would...
What is your source of information for the statement that "seaweed is mostly protein." I am pretty sure that for most plants, this is incorrect.
The best R&D in this area is conducted at Virginia Institute of Marine Science (VIMS) at William and Mary College in Virginia. I went to a presentation recently and was impressed. Although the industry is much more active in China and Japan, VIMS probably is doing more R&D than anywhere else...