Greetings, especially to Gilbere.
I would recommend anyone on interested in doing natural dyeing to join the Yahoo Natural Dyes group. It has over (?) 1500 members worldwide and is a mine of knowledge. I entered 'Tyrian Purple' in their search box and got 13 hits. Consensus is that the dye IS dibromo-indigo - it can be made synthetically and is carcenogenic (beware). The natural source is the Mediterranean Murex snail. (Great heaps of the shells have been excavated in digs near to Haifa in Israel).
The following link is also given in one of the references: http://pourpre.inge.free.fr/GB/recherches/recherches.html which makes for VERY interesting reading.
Very best wishes with this one!
Jenny of Cranbrook
(about 12 miles from the real Cranbrook, Kent. I did have a studio there for a little while in 2007. The Lady Ariel attended one of my courses there.)