this is actually something I know a little about. The reason that the time it takes to get sour very is is due to minor temperature fluctuations. Bacteria activity is highly dependent on temperature. Even small changes in temperature can cause bacteria to be more or less active. If you put it in a room with perfectly constant temperature you would find that you could get a fairly precise measurement of how long it takes to get sour
I would suggest one thing to you. Open up a few capsules of the probiotic that you have and mix them in with the cabbage. That bacteria in the probiotic will then quickly multiply. Then every time you take a bite of your sauerkraut it will be like taking five or six capsules of your probiotic. Then I might suggest to take four or five capsules of the probiotic along with your sauerkraut at the same time. The sauerkraut will provide a great environment in your intestines for the probiotic to fluorish