There are at least three known styles of JA signature canes, each being shown by Andy Dohan in his Signature Canes book (CD version). But there are also variations of apparently the same cane for at least two types.
Your first image is matched by the cane in a Perthshire Paperweights "witches ball" weight I have, except that in my example there are only 16 outer canes whereas in yours (and in Andy's book) the example has 18 outer canes.
Your second example is very much like one in Andy's book, with both having 25 outer canes that seem to be identical in structure and colour, but the actual "JA" in the one Andy shows is white letters over grey, but yours is grey letters over white.
The third type has thin "black" initials in separate white cores and these are surrounded by a 20-ribbed thick orange sleeve. The example I have was bought from Bob Hall and he illustrated it on page 137 of his World Paperweights book.
I thought I had added images of my examples somewhere in the GMB but I cannot find the message or the images.