Ideas how to clean mud/clay from Carboniferous specimens

[Steph]

Pottsville Formation, Alabama 
I would like to peek under the mud on the specimen in the first pic to determine if it is a compression fossil. This film on this particular sample seems brittle so I have to be careful. I can see pigmentation under some of the mud - that is where I want to work. Ideas? 
I hope I’m using these terms (carbon film, compression fossil) properly. 
I included other pics of other specimens that have carbon film or some type of mineral imprint (not sure what the term for this is) that I am to cleaning, sorting and comparing to potential compression fossils from Carboniferous. 
I was initially ignoring the specimens that look like pattern could be iron staining- thinking all were Liesegang rings, but I’m not sure that explains all of them. 

[Acb13adm]

Only advice I can offer is do it on some small broken pieces that are likely unidentifiable anyway. I was working with some pieces from the Valley & Ridge area, and they did NOT take well to cleaning. Still determining why, but at any rate it seems likely to be similar material from what I can tell.  If so, the layers will be soft and easily destroyed.

Good luck though 

[Steph]

On 8/7/2022 at 11:03 AM, Acb13adm said:

Only advice I can offer is do it on some small broken pieces that are likely unidentifiable anyway. I was working with some pieces from the Valley & Ridge area, and they did NOT take well to cleaning. Still determining why, but at any rate it seems likely to be similar material from what I can tell.  If so, the layers will be soft and easily destroyed.

Good luck though 

So true!   The top layer on the specimen in the 1st pic sooo fragile. That one is different than the others - the darker brown has a sort of a ‘texture’ (trying to think of what it reminds me of . . . kind of like pebble-grained leather) and is way more flaky than the others. I considered brushing the top of it with some type of glue. I’ve read that there are ‘peels’ of some sort, but ultimately I put it away until I can either figure out if it could be something or at least learn more techniques. 
I scraped some mud out of a few cracks on some of the others with a dental pic, but I think my curiosity will have to wait until I learn more. 
Thanks for your response!