Cansu

Which is really the temperature variable wearing a different hat. Every opening is a small warm-up.

Some of it is the nature of the thing, but four weeks is achievable and three variables decide it. In order of how much they matter:

Temperature, by a distance. Fermentation does not stop in a fridge, it slows down, and the rate changes steeply with a couple of degrees. A fridge that runs at 6 or 7 will take your kimchi through the same range in roughly half the time of one at 2 or 3. Most domestic fridges are warmer than people think and the door and top shelf are much warmer than the back of the bottom one. Put a cheap thermometer in the spot where the jar actually lives before changing anything else, this is usually the whole answer.

How far you take it before it goes in. Two days on a warm counter is a lot. You are handing the fridge a jar that is already well populated and well into its acid production, and the fridge only ever slows what is happening. Going in earlier, when it is barely tangy, buys you real time at the other end, because the whole curve shifts.

Sugar in the paste. The sugar is food, and it is the fastest food available. A paste with a generous amount of sugar or fruit gives the early sprint more fuel. Cutting it back slows the first two weeks noticeably.

Salt at 2 percent is reasonable and I would change it last, not first.