I can't give you advice, but based on experience, I can give you a bit more conflicting stuff.
The date of the sale will be whatever the ATO decides it will be.
This was often a point of debate when I was selling businesses. The effective time of the sale according to the ATO for property transactions is at the time the contract is executed, which of course is a nonsense because consideration has not been made and the contract has not been completed, and may not be for a number of reasons.
For other types of contracts, it is generally accepted that it is the date it is completed.
The sale of shares is contractually based, so my view, based on previous advice I have received, the effective date of the sale in your case is 30 June (T+3).
The Chess statement date is irrelevant as that has nothing to do with the settlement of the contract for the sale/purchase of the shares. It simply records that there has been a transaction some time ago and a transfer of shares.
Cheers
Country Lad