Maybe you could simply join a larger group and have Kalk tag along?
I'm quite certain that Kilo would not mind. Not to mention that Kalk isn't particularly flashy, so it wouldn't be unconceivable for her not to take a lot of space.
Perhaps Isabelle's? None of the people in it have posted yet, which would give Kilo some time to respond beforehand. You could simply introduce your character once they have.

Besides, there is nothing preventing you from making a post describing Kalk and your character entering the tower and surveying their surroundings...