Bea

There is no single right one, that is the point. Cooler and slower gives you a sourer, more complex kraut and much less risk of it going soft. Warmer and faster is fine and tastes flatter. If your counter is anywhere in the high teens you are already in a good place, you just cannot use the timings in a recipe written for somewhere else.

You have worked it out yourself: temperature is the main control and everything else is a detail.

The rates of everything happening in a ferment roughly double for each modest rise in temperature. So a ten degree swing is not a small variation, it is a completely different process running at a completely different speed. Your three weeks becoming nine days is exactly that.

It also changes which organisms dominate, which is why it affects flavour and not only speed:

Cool favours a slower, more complex succession. Kraut fermented cool is generally considered better and it takes much longer.

Warm is faster and can be one-dimensional, and it favours organisms that produce sharper, sometimes less pleasant results.

Hot starts causing problems, off flavours, soft texture in vegetables, and a greater risk of things you did not want.

So the timings in recipes are only meaningful with a temperature attached, and most recipes do not give one. A recipe saying two weeks is really saying two weeks at whatever the author's kitchen was.

Stop using days and start using signs. Taste, smell, bubble activity, pH if you measure it. That is the durable version of every recipe and it makes the swing survivable.