If it is true that Black has an unfair advantage, then the easiest coding change to make is simply to add a new rule on victory for White.
And as a game option, the original rules can still be played.
Please up vote if you agree or leave some feedback if you disagree.
Some reasons why there might be an imbalance between black & white.
1. Black has more pawns. This means that trading pieces, black get stronger.
2. To some extent all pawns get in the Kings way, which means that White should try an exchange or even sacrifice pieces, but this adds to point 1.
3. As time goes on Black get stronger. Blacks blocks and attacks right from the start which means White needs to act quickly. Black play very defensively / conservatively knowing his position is only getting better.
4. The corners are too easily defended. If White gets to a clear 2nd row then it's certain victory, but black can easily defend. Firstly 4 pawns start on all 4 2nd rows. Moving a single pawn to the 2,2 point means 1 pawns covers 2 2nd rows. Even when White looks to have attacked into a corner, Black can still put pawns on the 1,3 and 3,1 spot which makes it REALLY hard to attack. Even if white 'gets round the back' then it's often ineffectual to make any further aggressive moves.
5. In any given position, most moves for White will be the wrong move (piece just gets taken). And for Black it's just a case of enclosing, playing slowly and watching out for maybe 1 potential minor problem to defend.
All-in-all White can win, but only if Black makes mistakes. When black does blunder then it can be catastrophic which is where a lot of White wins may come from. But playing a game 'hoping' your opponent makes a mistake is not very enjoyable.
If black plays even just a reasonable game, then it is so frustrating for White and I wonder why I don't give up and start playing a different game.
The other common rule could be to allow the King to participate in captures:
So this statement suggests that may often have either 'King can capture' or 'White edge win' rule (but not both).In most games, the king can help to make captures like any other piece. There are some in which he can't, however. These are usually games in which he would otherwise be too strong: games where he wins on reaching an edge, and requires four attackers to capture him.