Well, I am totally clueless, but here is my thought. They had a giant concrete container box they initially lowered with a relief pipe. It was ineffective because the methane crystalized inside and clogged it.
Why not put it back in place while they pump mud and the golf balls in. The pressure will slow enough being contained in the container to allow the mud to start down the pipe.
Since the outflow is what is stopping them, slow the outflow first and then the plug will have a chance.
That makes more sense than what they were trying to do.