I have successfully bred in smaller cages; however, they must be suspended to ensure the ringnecks feel secure. If they are too low the birds will feel insecure.
I would however add about 3 feet in each direction on sides to the current measurements you have already given. It's important the cage be large enough to accommodate their tail, nesting box, food/water dishes, perches, and toys together. Believe me, all those items add up quite fast

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As for the nexting box, mine prefer ones that are deep. It allows them to feel secure when brooding their chicks. The nesting box should have a ladder installed to help the female climb up and down. If one is not installed, the eggs can easily be damaged as she jumps in.
Here is a great one taken from ringneckmutaions.com--very similar to the ones i use.
Hope this helps my friend!
Best Wishes,
IMRAN-C