I sprayed it down with CLP but I know there is a better product. The part inside the adapter will not move. Is there a product I can soak it in. Is this product safe for the adapter and the suppressor itself?
Thank you.

Have you tried taking it apart?
Below is a picture of my Trident with the original spring loaded 3 lug mount but I don't use it anymore since they do get fouled and stuck.
I just use the 'Bixler' design which doesn't use any o-rings or springs, never gets fouled up and locks up rock solid.
To clean the spring loaded mount, you need to get some kind of spanner wrench to go in that hole on the side and break it free.  Use some elbow grease and try to clean the carbon off.  You really need to take it apart to clean it properly vs trying to soak it anything and again there is an O-ring in there so some chemicals may damage it.  Again, why I like the Bixler design more.  No o-rings or springs.


Some info on my site:
https://c3junkie.com/?page_id=553

https://c3junkie.com/?page_id=777

Doing a search, I see someone quoted me on HKPro here: https://www.hkpro.com/threads/best-3-lug-mount-youve-never-heard-of-the-bixler-mount.536859/