In my opinion, the first reply you got provided the solution. Our younger son seemed occasionally to cause the same sort of "emergency" (of course not deliberately) for a time in his life, some toilets being more susceptible than others. The solution was always to empty a bucket as sharply into the toilet as possible and that did it on the first attempt in 99% of cases (too slow was the most common reason for failure). It is important to have no more water in the bucket than the toilet will take, band if the amounts match then you can literally tip the bucket upside down in an instant - but make sure you aim for the puddle because otherwise there may be a splash out of the toilet.