Knibbs in his book The Golden the Century a history of BSA guns has a picture of this action in the chapter on the No 1 and No. 2 action pocket model. It is is only described as different style of bolt and trigger mechanism in the Pocket models.

The number 1 and No. 2 were the same thing just with different fitments for sights. There is mention of the these guns being available in 297/230 Morris.

Knibbs book is poorly edited and is difficult to extract information from. I would not be surprised if the book has information on the OP rifle, but it would require reading page by page to find it, if it is there.

There is no BSA guns listed using the X prefix for serial number.

If you read Knibbs cover to cover you might find reference to activities in 1907, A search of BSA patents might disclose something also.

I also went through the BSA catalogs and could not find anything this gun.

This website seems to indicate this is a Model 2. https://www.rifleman.org.uk/BSA_Model_2.html

That website is you best resource for research on your rifle.