The "Deep Cleaning" process that I'll describe will take just a little bit of your time, a good gun cleaning product, I've used Hoppe's #9 for years, a good brass/bronze brush of the appropriate size, a cleaning rod, some good cotton patches, a well ventilated and warm work area that's protected from the mess, and some elbow grease.
This is the step-by-step process that I recommend:
Remove the barrel from the receiver.
Install a cylinder or improved cylinder* choke tube.
Spray the bore of your gun very liberally until it's dripping. I use a wide mouth jar filled with Hoppe's #9 and dip my brush in it from time to time to keep it wet. I “scrub” the barrel from the chamber to the muzzle end for several minutes. I recommend no less than 4-5 minutes. Really scrub it and use additional Hoppe's on your brush and in the bore, as needed, to keep it very wet. DO NOT SWAB IT OR DRY IT.
After your scrub, for at least 4-5 minutes, longer is better so don't cheat on the time, let the barrel set wet, don't swab it, for at least 10-15 minutes at room temperature.
After you've let it set, scrub your wet bore again with your brush for a few minutes, use more solvent on your brush and in the bore to keep your brush wet and to help “wash” your barrel while you're doing this.
Now, it's time to use the cotton patches. I usually switch to a Tynex bore brush for this operation but you can use an older brass brush. Place a patch over the brush and swab your barrel until at least 1 patch comes out clean and dry.
Remove the cylinder or improved cylinder choke tube you installed and clean the area that it occupied, including the threads, with a toothbrush or brass brush made for this purpose. (You should always keep some type of choke in your barrel to prevent foreign material from fouling the threads). Wipe the bore dry with a lint free cloth. Look at your barrel. It should be shiny and bright.
Reassemble your gun.
If you're ready to pattern test it now, leave the bore dry and install your turkey choke. If you plan to store it, you may want to put a protective coat of lubricant on the exterior and the bore of the barrel. Be certain to remove all lubricant prior to shooting.
This process involves some work but it will pay dividends in most cases by helping to increase the quality of your patterns.
Lastly, be certain to read and follow all label directions and cautions on containers regarding disposal of rags, newspapers, etc.in a responsible and safe manner.
*This is done to make it easier to clean the barrel. It is sometimes difficult run a cleaning rod, brush or patches through tight turkey chokes. Ported chokes can be hard on brass brushes and sometimes "eat" cleaning patches. You should clean your turkey choke with at least as much care as you clean your barrel.