Hi :) Just to let you know I'm only on page 1 of your thread, as I'm tired and it's making me feel a bit wibbly. You may have already moved on or someone might already have said ...
Two things I've done are "empty chair" and "black & white movie". You do both of them by yourself. I think I would do the movie first, then the chair. In both cases, make yourself very comfy and calm in a safe place where you won't be disturbed.
Imagine you're at a cinema of your own perfect devising (could even be where you are sitting, though mine was a little private cinema I sometimes went to in London). You will probably want to imagine you're alone, but have a security guard or similar there if you want. The movie starts shortly before the incident in question. It is all black & white and filmed from some distance - this allows you to feel detached from the images on the screen. You can slow down, fast forward, pause and rewind any time you choose. Watch the events leading up to the incident, taking care to feel your comfortable seat around you and keep breathing with slow, steady breaths. If you start to feel panicky, stop the movie. You can come back to it whenever.
I watched the beginning of my 'movie', then the end. After that, I wound to the middle of the incident and watched a tiny little bit. Then I watched the beginning in slo-mo and the incident in normal time. As this is an 'inner child' therapy, I then put my own self in the movie and comforted the girl who suffered the incident (me), thus changing the final reel by helping her to feel safe. I can recommend doing this, several times if possible.
The empty chair is just that - place an empty chair opposite your comfy place, facing you, and talk to it. There's no need to imagine any person sitting there; I give it a vaguely warm, wise, compassionate presence but you can leave yours as exactly what it is: an empty chair! This is far more helpful tool than it sounds ... though I'd make sure there's nobody looking through the window when you talk to a chair 
I agree that your therapists sound weirdly obsessed with your naming the traumatic incident. I hope you find techniques that are helpful to you, and one day you will be able to name it without retching. No need to rush towards it, though :)