My suppressor is still in jail, but I use this method to clean the comps for our race guns, should work for suppressors.
What bothers me about this method is handling and disposing of the peroxide/vinegar solution (AKA the dip). What is left behind after soaking the muzzlebrake or baffles is lead acetate. Just reading about that stuff scares the heck out of me.
I use to clean the rimfire baffles in a tumbler with steel chips or pins with Dawn dishwashing soap and citric acid / Lemishine. That got them really clean except the caked on lead residue was a PTIA to get off.
Instead of using the dip, I boiled the baffles after tumbling, in cleaning vinegar outside for about 30 minutes. Then I let everything cool.
The lead was turned into a light gray powder residue that I could scrape off with a pick. I suspect that was lead acetate in powdered form. Nevertheless, I would rather handle that stuff with proper PPE in powdered form rather than liquid form.
The above is what I use to do. I found something even better. Watch this video. He will tell you a lot of what you already know but skip to about the 9 minute mark to learn about the treating the baffles with silicone oil.
Hopefully, you have had a chance to watch the video. I gave all of my rimfire baffles and handgun suppressor baffles the silicone treatment. Before that, however, I made sure that every speck of lead was gone from the metal surfaces.
Instead of DOT 5 brake fluid, I used pure silicone oil.
After about 300 rounds of use, there will still be a lot of carbon deposit and residue on the treated rimfire baffles. I could wipe everything off with paper towels, cleaning patches and q-tips for the tight spots. If there was any carbon deposits remaining that the cloth and q-tips could not wipe away, I used a metal pick to flick them away.
Keep in mind that there is none, absolutely none of the caked on lead as before.
After each cleaning session as described above, I would put liberal amount of CLP on the baffles and inside the can itself. Some people may disagree with how much I put on the rimfire baffles but running these things really wet, combined with the silicone treatment, seems to help with cleaning afterwards.