I forgot about that. It is risky to do but when in Cross’ suite, you can go up the stairs and either lure Jordan into one of the rooms with a distraction or confront Jordan Cross with the tape.
I think the canon way to kill Jordan Cross is to disguise yourself as the drummer. Check in the to hotel and go into your room. On the balcony, there is a drainpipe. Climb down the drainpipe when no one is looking and hide in the empty lounge. You can distract the drummer as he is on the balcony into the room. Throw a coin and get his disguise. Then head to the Jordan Cross wing and approach Jordan Cross. There will be an opportunity where he will go to the atrium and you can push him off.