Yes, the XL transilluminator does fit inside the imaging enclosure. It is a snug fit, but it works. Unlike the Small, Midi and Large transilluminator, you do have to take the door off in order to take the transilluminator in/out of the enclosure. But if you are planning on keeping it in there most of the time this shouldn't be an issue I would think.
There is an adapter we ship with the XL version, which is not a frame but a base plate for the transilluminator to sit on.
I have added the Extra Large XL option to the product page now, so you should be able to select it.