I have actually done therapy in a gyneacologist's exam room - on the table - once, although I didn't use the stirrups. (was shortly after my leg amputation. Sitting hurt a lot and I couldn't for more than an hour or so at a time, so I asked her to arrange a room where I could lie down during the session (as I'd also have to sit in the car during the trip). This was the nearest empty room.) x)

Would it be possible to start the sessions in the room, then when it gets too much you'll take a walk outside or sit on a bench or something? With your T, I mean, to continue the session from there. Or just to calm down and then go back to the room.
Maybe it would also be helpful to go slow, I mean, don't feel you have to continue the regular heavy therapy-y stuff immediately in the new room. Take some sessions to acclamitize the new room. Look in all the cabinets if it'd be helpful. Chat about the weather. And then if after a week or a month or two months you'll feel more comfortable, start talking about things that matter. Then about upsetting things that matter.

For you (and the rest of us), therapy safety is a triad: yourself, feeling safe with the T, feeling safe in the room. If you go to see a new T, no one will expect you to bare your soul immediately. The room is also a part of the triad: so no one should expect you to bare your soul immediately in a new room.