I've not had much experience of blocked toilets I'm glad to say - solving them has been limited to pouring a bucket of water in from a height or using a plunger.
I had to do one recently that was really badly blocked and I used a drain unblocking hose attachment on my Nilfisk pressure washer.
The strange thing is that once it was unblocked, when I flushed the water level ended up much lower than normal and there was a kind of "motor boat" burping sound!! Now even after a few flushes the water level always ends up a fair bit lower than it should be.
The toilet is ground floor, goes sharp right after pan, along half a metre, then sharp left then through some kind of boxing in and out through a wall 23 inches thick to emerge below ground level outside where it joins the soil pipe from upstairs.
Background: we just had some professional drain jetters in as the pipes were blocked by sand (seaside location!).