I'm not surprised that this question has remained unanswered for so long because 'Clay' is possibly the most difficult story in Dubliners to interpret with any degree of certainty. I personally am not even sure how seriously to take the story, my main reason being the insistently cartoonish way in which the central character Maria is presented. Joyce tells us three time that the tip of her nose nearly reaches her chin, an anatomical impossibility for most human beings: the only way I can visualize it is by imagining a witch in an animated film or a children's book. If that's how Joyce wants us to see her, it is hard to work out any theme from that basis. Yes, it is Halloween - or Hallow Eve, rather - and there are cauldrons in Maria's workplace, but Maria is otherwise associated with goodness and religion, so where does that take us?
Another mystery for me in the story is the number of things lost or mislaid, the nutcracker, the corkscrew, one of Maria's cakes, the verse of the song, and of course the objects hidden by blindfold in the game. This seems very deliberately done on Joyce's part, but to what purpose?
To see how carefully and deliberately the story is written, look at its structure: 19 paragraphs, eight each at the two main locations and three consisting of the journey to and from the centre of Dublin and the purchase of the cakes. It is very symmetrical and interesting but again, to what purpose?
Finally, there is the title and the meaning of the clay in the story. I have read some fanciful interpretations seeing the clay as Ireland being moulded by England and the quarrelling brothers representing the fractious, divided Irish but I haven't been very convinced by anything I've read about 'Clay' and in fact I think I quite like it that way:I still read the story from time to time and enjoy its mystery.
Sorry to have written a non-answer rather than shed light on your query, but if I've managed to give you something more to think about maybe it's worth it. Good luck.