No, no, no! Do not remove the breach plug!!!! You don't want to remove the breach plug when there are other options. If you happen to have a CVA rifle, you never, never, never mess with the breach plug. The best suggestion is the one from 54ball about using a copper pipe or tube to remove the brush. This little trick has almost become the standard method for removing a stuck brush from a bore.
Once you have it out, do not use it or any brush in your bore again. These things are fine for modern guns where the breach is open and you just push the brush through. But when you are dealing with a muzzleloading rifle where the breach is not open, a brush is almost guaranteed to get stuck. There is a technique for removing a brush from the bore as long as it is still on the rod and that is to turn it clockwise to cause the bristles to lay down. Then as you continue to turn the brush as you withdraw it from your bore. But, in your case, the copper tube is your best bet.
If you use nothing but patched round balls, as God intended, you will never have a leading problem. The only thing that will be in your bore will be black powder fouling that is easily removed with warm soapy water and patches on a cleaning jag. No brush will be needed.