I managed to dig out the tools I was on about, just to show you how awkward they were to use:
The inner lock ring hook tool was difficult to get enough leverage, as the shape made it awkward to hook on the cut-outs properly. The hook would slip out frequently, causing a few expletives.
The outer lock ring tool (and I was correct the first time) was just too fat in parts to squeeze between the lock ring and motor casing. This meant you only had a tiny window, where the tool was thin enough to fit on and turn.
The all in one tool that I use nowadays, just makes it easier, even after the requirement to remove the crank arm or pedal.