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Besides Shafran's chess, another remark deserves to be added to Brusky's chess, which in my opinion is the closest possible translation of chess to a hexagonal board. The problem with it is the fact that the number of pawns there is not equal to the number of major pieces, and the fact that there are also forced defensive progressions from the very first move, which makes this variant unsuitable for high-level play. The pawn's movement rule was also slightly modified to make the variant stable.

It can be forgivable for Capablanca Chess or that Shogi variant revealed by H.G., but they are not as significant as hexagonal chess by their nature, I cannot see them being independent of Western chess and Shogi respectively. I'm not a shogi player again, I know nothing about it.

We are interested in hexagonal chess variants because they are played on a fundamental tesselation. As can be expected there are not plenty of tesselations available. So it should not be regarded as a variant of chess, but rather, another chess. To get the idea, I do not play chess because it is fun. I play it to find fundamental feelings of mathematics, or at least an illusion of them since chess by itself is an extremely artificial game, with plenty of questionable rules. But still, the roots of it are still fundamental, we can get them. A search of something initial.

So I would try to end my search for hexagonal chess on Glinski's chess. Yes, the pawn is a problem, but at least, this variant is not flawed. If chess was already full of artificial rules, the modified pawn can be seen as a slight extension (at least, there's no castling anymore).