Another way to test if the Koh-i-noor would fit into the space where the Cullinan IV was inserted into the tiara is to look at the physical dimensions of both stones. (I will not bother with the depth of the stones as that would not be an issue in this tiara)
The Koh-i-noor measures 41.74 x 33.89 mm.
The Cullinan IV measures 26 x 26 mm.
Although I am only guessing, it seems to me that there would not be sufficient space to accommodate the the Koh-i-noor.