The Solution, in this case, was not to use a Hough Transform at all.
- I used a threshold and blob detection to find the outer circle which gave me the centre.
- Then an horizontal-intensity histogram to find the peaks that correlate with each ring
- Then compare this against the peaks from a vertical-intensity histogram, to get the radius of each ring
- Then some sanity checking.
I haven't got the peak detection working yet, but it's in progress and it all looks like working.