Having shot slugs in quantity for years at work...here is what I found works-
Assuming you have a pump or semi auto where you can remove the barrel...don't get anything on the wood.
Start with something basic like hoppes # 9, soak the bore and brush with a Bronze (not steel) Tornado brush. Don't bother with the bristle brushes...they suck. Wet it and push back and forth 25 times or so. Use a coated rod to prevent scratching the bore. Watch on exit that you don't drag the edge of the rod against the muzzle or similar.
Patch dry...inspect.
Now, Slip 2000 Carbon Cutter is your friend. Soak the bore...and I mean soak. If you could plug it and fill it...it would be great, but it's not needed. I just keep a rod with a wet patch on the bench and run it through every 30 minutes for a day (Saturday). After 4-8 hours, brush, patch dry. This will get all carbon out.
Now...you likely have a bit of lead and plastic to get out. Nothing cuts lead chemically except some uber nasty stuff that will kill you as it makes the lead a solution that is absorbed transdermally. Wear 2X gloves if you try that and trash anything that gets wet. Better to go hard after the plastic and scrape at the lead with a Tornado Brush. For Plastic...GM Top Engine Cleaner, Carb Cleaner, Gun Scrubber...or similar. It evaporates...use a lot, use it every 3 seconds, and scrub. Wear eye pro.
For chokes...remove them, soak in a jar of carbon cutter for 48 hours, scrub, lube, install. Always grease the threads on choke tubes.
Finally, patch it with a light oil like Break Free CLP to prevent rust.