'tis a delemma. Do you wish you had not mixed rye with KBG? Maybe you could have seeded the KBG first and waited 2 weeks to do the rye. This is always an issue when two or three seed types are mixed.

Continue watering 2-3x per day or you will have no KBG at all.

As for mowing you are really walking a tightrope. You can mow anytime up until the KBG seed sprouts. Once that happens you need to stay off of it or you will break the seedling KBG plants. And if the grass gets upwards of 5 inches in the mean time, the rye might provide too much shade for the new KBG seedlings. I would give it 5 more days and mow it back to 3 inches unless that rips the rye out of the ground. Continue watering like that until you have 80% germination of the KBG and it is at least an inch or two high. Then you can back off on the frequency and go up on the duration.

On the plus side, you only need a few KBG seeds to survive, because it will eventually spread to fill in any thin spots.