There was nothing the opposing Princes could do. Directly after Kwan's turn, it would be Ryu's turn to go. There were no more opportunities to interfere. Although they could theoretically attack Prince Kalmin, the only individual who could do so was First Prince Amory. Since Amory was on his seventh step thanks to Atticus' help, he could use his three actions to finish this trial out. However, if he used one of his actions to attack Kalmin's step, he would be giving up his right to place second!
Since Kalmin could never do that, he would have to concede to allowing Ryu's plan to continue unhindered. In this way, Kwan, Kalmin and Ryu would have the smoothest turns of this entire trial, this was especially so for Kalmin who had seemingly accepted a pie that descended from the skies.