The most important part of your question that I think everyone has missed is;
What you described and what you did on your IR test was not a circling approach.
What you did is an ILS to minima followed by a single engine missed approach which was converted into a visual circuit.
For a circling approach, your minima would have been the circling minima i.e. an MDA(H) and you would have flown level at that MDA to the MAP Pt if not visual. Or you would have flown at that MDA(H) on your circuit to land.
If you have problems maintaining MDA with one engine out then can you shoot any approach in reality?
DFC