David,
thank you for the connection to the Carol Floate site. I'd seen her work before but never realised it was marbling work - but it is stunning.
Soon after I found my boxed set, a member of one of the clubs I attend (and a sometime contributor to this forum) produced a couple of pieces, they were the only work like this I'd seen.
The system was used years ago to produce those wonderful old book inner leaves. So the methods to do it are old, as are the pigments and other requirements. It is probably that oil paints were used once, I remember doing something like it at school (too many years ago).
Now we use acrylics so I'm quite sure the stuff added to the water (I thought alginate but you say carrageenan - thanks for the correction) will be different to the old ways. Though a look at Wikipedia shows that they are both gelling or thickening agents. Which I imagine is what the Borax in my box does.
Also if you look in craft shops there are so many types of pigments available, from the oil, alkyd and acrylic paints to alcohol based inks and stains, there is lots of room for experimentation here.
Maybe we need to find a modern day bookbinder and ask what they do!