I noticed the same thing. I was able to really boost my score by just drawing over the 'same' circle a bunch of times. Doing that got my score up into the 7-8 million range.
I believe this website is using what the paper calls the geometric fit, which is considered one of the better methods, but the paper develops an even better method.
(I had to use this, strangely, in a physics lab course. I was measuring the Zeeman effect by looking at the diameter of rings of light projected by an interferometer; I took webcam images of the ring and used the algorithm to fit circles to the ring and hence measure its diameter.)
Using a Hough transform to find a circle with an unknown radius is expensive. You have a 3D parameter space, and each point has to "vote" for a 2D subsurface of that space. Discretizing the entire volume at a high resolution is going to require a lot of memory.
I agree it is going to expensive but it's not because of memory. You could probably just try every (x,y) center and have all points vote for the radius, and just keep max before moving on to next point.
A sensible, easy thing to do here seems to be to just find the centroid of the cluster points. Then convert all the points into polar coordinates around that centre, and average the R's. The R's could be weighted rather than taken at face value.
This make me remember the Giotto big O history [1]. The pope was looking for a painter and requested samples to artists and Giotto sent for him just a circle.
A smattering of poits scribbled close together nets me 220000, while a single big ring earns only 700.