It is true that Hajdamach offers evidence for Richardson using false "1848" canes. However, the bottle shown by Hajdamach (page 408, Plate 372) from the Hill Ouston catalogue differs from that shown by Roger. Roger's has a foot rim with a substantial distance to the lower part of the body, but the Hill Ouston one seems to have no foot, even though footed items are well known in pieces attributed to Richardson. The neck rim in Roger's is thinner, wider and less rouinded than that shown in the book. The stopper in the book example is indeed shaped much like those seen in many bottles attributed to Richardson, but Roger's has a stopper that is not as wide as the neck rim.
In fact in Roger's bottle the stopper seems to be leaning over and may not fit too well. It could be useful to see a photo of the canes in the stopper - it is not unkown for stopers and bottles to get mixed up!
In the book, Hajdamach quotes some cane colour details from an original document that helps to suggest a Richardson link. But the colour descriptions such as, "centre white ruby outside, amber white outside ..." could just as easily describe canes from any "old English maker, including some used by Bacchus!!
I agree with Alan that Arculus / Walsh is not an easy separation to make. I see no reason to think that Walsh would not have used existing cane stocks from Arculus when they bought the company, and therefore cane matching can not always lead to the right attribution. I think Roger's bottle could be either.