As the title says, looking for a rod that will be stout enough for removing barrel obstructions. A lot of our training involves sims and occasionally we are knocking out 4 or 5 rounds stacked up in the barrel. Would like something stout enough to hold up to this but won’t damage the barrel.

Does it exist?

I have a few brass rods in common bore sizes from McMaster-Carr, in Marine Grade 485 brass. Soft enough to not mar the bore, yet tough enough to push bullets out.

This. ^^^^

Ok probably gonna go this route. Thanks guys.

FPNi. Dont use steel. There are carbon fiber rods that are good and also any brass rods will work. They're both softer than barrel steels.

The trick is that the brass rod needs to be a fairly snug slip fit in the bore.

If the rod is loose, as in doing what too many people do and use a cleaning rod, the rod is free to bend and flex and dissipate the force.
If the rod is a snug fit the rod can't flex and all the force goes to the obstruction.
Also, the rod can't slip off the obstruction and gouge the bore.

The rod end needs to be flat on the end with a slight bevel of the sharp edge.

In a rifle, you might need short sections instead of one long rod.  If you put a long rod into the barrel and too much is sticking out the rod will flex and bend.
To use sections, just insert as many as needed to get to the obstruction and add sections as the obstruction is pushed out.

I can't guarantee safety or the wisdom of my method, but I have sprayed a little oil in both ends of the barrels with two stuck bullets and fired a primer seated in a once fired case to drive them out. Virtually silent, point it in a safe direction outdoors.

Primers have more power than most people realize. No powder! No projectile! The oil is needed and allows the bullet to move more easily.

I keep a GI rod in my range bag for just this occasion

Yup.

Best advice so far.  Well said.

Best course of action.

I use a 3/16 steel drill rod.

No, I do not worry about damaging the bore, and no, I do not take it to the range.  If I worried about either, I would first consider using more reliable ammunition.