Good comments above, here are mine for what they are worth.
Don’t “scream for help.” Yeah, I know, I’m being picky about words, but seriously, in in any emergency, you have to minimize your own stress response. How do you do that? Good question; glad you asked. You do that by acting calm even though you do not feel calm. Take a deep breath (yes, you DO have time, as discussed below) and call for help in a clear, slow, controlled voice. You will be faking it, but that does not matter. Behave as though you were calm, and your behavior will change your emotion; which works better and faster than trying to control your emotions directly. Really, this works.
I agree with moving the patient to the floor if transfer to bed is difficult or time consuming. You do not know, initially, what is causing the crisis, so the safest thing is to supinate the patient because it facilitates circulation. Since lowering a heavy patient is easier and faster than lifting that patient, I go for the floor. Better to use gravity than to fight it, whenever you can.
You might be able to save those IV, arterial, and pulmonary lines if you can put the equipment or pressure bags that they are running on the floor too, but that depends on what kind of equipment is in use. If you carry a couple of straight Kelly clamps (which I suggest) you can clamp them, disconnect them and position the patient. Yes, I know, that is dangerous, both in terms of sepsis and clotting, however, losing access in a crisis is also dangerous, and, once the patient is back in bed, you may be able to use them (and, trust me, you will probably need every line you have). It is a risk/benefit decision that you just have to make on the fly.
MOST IMPORTANT OF ALL: Do not allow yourself to get frantic by trying to do everything at once. Do not become agitated because it is taking what feels like a long time to position the patient. Your sense of time will be distorted. Again, ignore your feelings, concentrate on doing the one, next, necessary thing, and do not try to rush. Bottom line: if the patient dies in the 10 – 20 seconds it takes for you keep things under control, you could not have saved that patient anyway. I am sorry for how harsh that sounds, but it is true. If you try to manage everything at once, you will quickly loose control of everything. Taking it one thing at a time gives your patient the best chance possible.