Pete - Don't know whether you have the small booklet "The Story of Edinburgh Crystal' from Dema Glass and written by H. W. Woodward - really a potted history of the C19 and C20 history of E. & L. and then with the name change in 1955 into The Edinburgh Crystal Glass Co. Very interesting, but not something you'd buy if you wanted to research glass patterns or designs of Edinburgh Crystal - apparently those are in '14 substantial volumes', and were at one time at Penicuik, although may now be at Broadfield House Museum, and I believe are mostly (if not all) the earlier pre name change patterns. Presumably these would cover the period of your four E. & L. glasses (for which you don't have a name), and which you say are 1929. Now you have the Replacements webb site, you might try looking for them again - should I see them I will let you know.
As for the expression 'brilliant cut', I have an E. & L. dessert (or similar) bowl on stem, which is cut deeply all over the bowl, which I thought was the qualification for brilliant cut, but not sure. Originally, it was a description from the States in the late C19, which then spread to Europe, but when we all got fed up with cut glass it seems to have disappeared.
I really don't know where or how the Replacements Ltd. people found their images and data shown on their site.
As you say, your mark is the post 1955 back stamp when the company had become The Edinburgh Crystal Glass Co., although how much 'post' I don't know.
P.S. To me there seems always the potential for confusion with the expression 'Edinburgh Crystal'. On the one hand it is simply the name given to lead content cut glass produced in Edinburgh, by several companies (including E.& L.) and then there is the possibility that it might be referring specifically to The Edinburgh Crystal Glass Co.........ughhhhhh