I received a piece of limestone matrix from a quarry near St Petersburg containing an asaphid trilobite. I'm giving it a go. Not complete, but pictures of the progress thus far.
The initial state of the matrix above.
This one has been a bit of a challenge. A lot of the matrix is nice and soft, but there are "sticky" bits. I knew that the piece was not going to be museum quality, so I expected there to be a bit of damage. The thoracic area at the axis was already missing some shell, so I was not surprised when uncovering the rest that it would be missing. Unfortunately, I don't have any spare pieces of this to attempt a minor restoration.
I did goof in one area, breaking off a bit of the shell. After uncovering the bulk matrix and performing some pin prep, I stabilized some areas with crazy glue, used the air abrader, and then brushed acetone on it to remove the gobs of glue. A few more pin prep attempts and I think this will have to be about it: