Based on the information provided in the article, as well as the illustrations and descriptions, my sequence of the stirrup spout bottles arranged as follow:
Vessel A, C, B, G, J, I, F, K, D, E, L, H
This sequence is based on the distribution of features, and it looks like the proportions of the vessel body tends to get bigger, and the decoration occurs on either the neck or the body is getting complex by the time. Also, there are some slightly changes in details of these vessels, such as the stirrup and spout, but these changes seem to occur periodically.
Initially, I feel that vessel A is quite different from the other vessel and seems does not fit into the sequence, because it actually has many similar features with other early stage vessels, but have much more complex decorations, and these decorations are different from the ones at later stage as well, as some of them are appliqué, which only occur on vessel A. But there exists a possibility that vessel A belongs to the very early stage, and due to the limit of technology, they cannot paint or decorate the vessel directly.
Another vessel looks do not fit into the sequence is J. Among all the vessels, it seems the bands decorations actually came much earlier than the boarder body. However, vessel J has very initial decoration as well as a board body. So I think the vessel J might be another direction of changes along with someone else and appear at the same time period, as two experimental products.
Also, these vessels do not seem to fit into the sequence might came from another civilization by trade and exchange. And some of their features mixed with the original vessels later and make up the sequence together.
I think there is some features that indicate their actual time period, and I actual determine my sequence based on these features. I made a list of these vessels and their features, and the descriptions look like permutations of some groups of key words: whether the spout is tall or short, massive conical, concave-curved, or straight-sided; whether the rim is flanged, or beveled, and etc. And these features could help us arrange their position is the time sequence.
I think the establishment of this sequence is quite similar with the seriational ordering before. These figure is obviously unique among all of them, but have many similarities here or there. And these similarities could help with link two or three of them together, and make a roughly sequence. Some of them might not fit and would need more consideration to be put at a suitable position, or think about a reasonable explanation.