Hugs foxy - I know how frustrating and infuriating it is to have to sit with an LO while they just mess around and fidget instead of falling asleep!
When I was doing GW with L, some one suggested telling her I was going to leave the room for a minute to do xyz and then return, and gradually increase the amount of time away from her. At the time, I tried it and it didn't work, she didn't want me to leave for a second so I didn't push it. But I have used that tactic a couple of times recently when L has EW and hasn't wanted me to leave and had more success (ie I've been able to leave her w/o her screaming). She's also 'let' me leave if I offer to leave her door open a bit.
Perhaps this is something you could try at BT? If she cries straightaway then you could go back straight away or after only 10 seconds or so. But if you do it for a few evenings, perhaps she will learn that you DO come back when you say you will, and not be upset if you go. Of course, you'll still have to go back but you could gradually increase the time you are away and it might get her used to not having you around the whole time she's settling. Leaving L's door open a bit (when I leave) also helps if she's upset - she's usually happy to let me go then. Just a thought.