You're quite right, Dryden. There are 2 down entries starting from the 2nd row, neither of which share a number with the across entries. So the first across entry in the 3rd row is 17A, the down entry is 18D.
For the digits going into the central cells, I've simply added one to the series given by the thematic groups. Which represents 3 days after the solstice - close enough to warrant a celebration I suppose...