I obtained an SD about 2 mos ago and have put everything 124 gr or less through it I could find.
I'm compiling a speadsheet of various data, but even the "cleanest" ammunition still makes the SD pretty filthy.
Solvent tanks for final cleaning, with a bottle brush, and scrape out in the reciever/trunion area with a pick, as carbon will really build up in that area. I have an old dishwashing brush I use in the field to periodically clean out the reciever body and wipe down the bolt group.
++ on the brush, or if you can find a hollow battery brush and adapt a length of PVC tubing, just be cautious of any steel against the threads of the actual suppressor tube.
Carbon Killer works good to keep it clean in the tube, as well as periodically using the well engineered HK method of banging against a wood block. I'm surprised HK doesn't sell a specific wood block for SD cleaning.
I use a very light touch with a nylon bottle brush, followed up by laquer thinner to displace any remaining moisture.
Cautiously scrape out the area in the tube where the ports exit, and ensure none of the ports are clogged.
I believe I heard that RDTS sells a fake suppressor that is able to allow firing of the weapon, that the fake can is machined so that it bears against the ports and seals them.
After a few hundred rounds, you'll see where it gets nasty and it makes for a good excuse for a good shoot em up movie while I clean the weapon.
My personal SD cleaning movie is Tombstone.