Pete,
I believe that the information you gave is for Rust Bluing, in Rust Browning you omit the boiling. The boiling is what gives it the blue/black color. For the Browning of Damascus it would still take as many rusting and etchings to produce the color desired.
The last process mentioned from Parker's Factory Process doesn't mention boiling so might be browning but you would need to be a chemist to figure it out.

Wanted to mention also that I like your site and your commitment.

David