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.