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Deciding who moves first: In Chess and most chess-like games, the first move is always given to one side. In Chess, the side with the first move is always White. However, the side with the first move also has first-move advantage. In Chess, White has a slight statistical advantage over Black simply because White always has the first move. Because either side can move first in Yangsi, that slight statistical advantage is eliminated.

You make it sound like this is an advantage of this game, but it isn't. The first move advantage still exists. While it no longer belongs exclusively to one color, the new rule concerning who moves first doesn't change how frequently the actual players each have this advantage. I would recommend scrapping this rule, because it does not actually make the game any fairer. It is simpler and better to just follow Chess on this one and let White move first. How the players decide who will move first would then simply come down to how they decide who will move as White.

While I'm glad that Gross Chess has played a role in igniting your interest in Chess variants, I have my doubts that reducing the size of the board while keeping the same pieces will make for a better game. The opening setup in Gross Chess is designed to give most of the pieces a little bit of freedom of movement from the very beginning. That gets lost with all the pieces crammed together. Also, this game has 60% piece density at the beginning of the game, which is higher than the 50% in Chess or the 64/144 = 44.4% in Gross Chess. This might make the game more cramped. However, I haven't done any extensive study on how piece density affects game quality, and I'm only guessing that higher piece density could have a deliterious effect. Some actual gameplay is required before I can make a more considered judgement on this matter.