Years ago when working up squib loads for the kids and when I had free daily access to a virtually unused indoor range, I stuck a few bullets, both jacketed and cast in .223 and 308 barrels. This was in the course of thousands of squib rounds fired in the range, so it does happen.
A moderate cast bullet level charge will shoot the bullet right out. In fact, a heavy charge will work just fine if your backstop will withstand more powerful ammo. As I posted earlier, there is no radical increase in pressure and probably a reduction in pressure given the expanded volume of the chamber which now includes the portion of the bore from the chamber to the stuck bullet. It is, as Larry points out, a breach seated bullet and poses no more danger than that. To expedite the departure of the stuck bullet, clean and lightly lube the bore in front of the stuck projectile.
Remember that this isn't putting a bullet down the barrel against an obstruction or stuck bullet. That is frowned upon!
I just can't get behind pounding a rod down an expensive or unobtainable original barrel with a hammer.