If still in IMC at (say) 800ft in an approach with Circling Minima of 700ft you would need to start the level-off in order not to bust minima. But is that really acceptable if still IMC? Isn't a GA in fact necessary by then?
No, it's different to flying a CDFA for the purpose of landing straight ahead. In that case you would commence a missed approach immediately if not visual at the minima. However, if you are flying an approach with the intention of circling, then you can descend to the circling MDA and fly level at the MDA (but not below!), but you don't need to commence a missed approach until you reach the missed approach point. That may not occur until you're overhead the navaid or even later, depending on the design of the procedure and the location of the navaid, etc, etc.
For example, the VOR Rwy 16 at Fukuoka in Japan is based on the DGC VOR, which is located 5.5nm before the threshold of Rwy 16. The missed approach point is located D5.4 after DGC, ie just before the threshold of Rwy 16. If you were intending to circle for Rwy 34 in a Cat D aircraft, you could
theoretically descend to the Cat D circling MDA (1030ft), then fly level at the minima until you reach the missed approach point, then execute a missed approach if still IMC.