I disagree.
If you go round on final from a circling approach an you still have required circling vis and are with in circling area you can climb back up to circling minima and do x-wind / downwind and final.
Happens all the time in the sim when I screw up the turn on to finals and decide to go round.
Leave gear down, gentle climb back to 1000 AGL (or whatever the circling minima puts you at) and round you go.
In all my years have never had a sim instructor question that approach to a missed approach from circling..
You can circle in the circling area until the cows come home as long as you satisfy the vis/obstacle clearance, circling area etc etc.
During the mised approach up to circling minima , yes you cannot see the runway etc but in that portion you are conducting a missed approach with all the assoaciated climb gradient requirements. Once AT the circling minima , if you are still within 4.2nm (cat C), you're good to circle around for another go.
If you enter cloud...different story of course....you must carry out the whole shebang..ie shortest turn towards the aid and carry out the published missed appraoch.