I think we can safely assume that the Greatstone battery (415) was already there in September. Entry from the War Diary of the 7th Somerset Light Infantry (WO 166/4658), which was holding the Greatstone-Littlestone sector:
21.9: “All Coys concentrated on finishing the wiring and setting beach mines on the Sea Front. This was finished to Right Boundary. At 0930 hours an Exercise was held of 4 landing parties attempting to destroy the two six inch guns and testing A Coy defences and the No 6 Commando counterattack. The Divisional Commander attended.”
This entry cannot refer, I submit, to the St. Mary's Bay battery (358) because that was in the sector of the 6th SLI.
In any case, it would have been strange if the Siting Committee (as I believe it was called) had ordered the batteries at Hythe and SMB to be installed in June already, and had then further South left a gap in the gun coverage of this important and vulnerable coastal sector until October.
That said, the numbering of the Emergency Batteries remains a mystery to me - one would expect them to be numbered in batches as they were planned and constructed, but the no. 416 battery at Jury's Gut was in fact not ready until early October; as noted before.