Firstly, Z does EPI (Early pay-in) so there is no 3 days. Shares will be deducted on same day of sale.
More importantly, Do your LTCG calculation from contract-note Dates OR demat-to-demat dates and dont get tangled in the backend complexities. There has been such cases before and court ruled in favour of contract notes dates also.
So ensure you are selling on10-jun, the 366th day as LTCG says “more” than 1 year.
If you intend to re-purchase, again wait for 1 day and ensure the Demat is actually debited with old shares, otherwise STBT ( BTST ) may not actually debit and that is another tangle that one can by way of proof sort.
Basically, your accounting practice has to be consistent. Then you cant use BTST/STBT as separate case(STCG) and all transactions will be treated as FIFO,
Yes, next day should be ok because EP-IREM is recorded in Demat statement on same day of SELL even though the debits are settled as per settlement cycle.
Yes, I do not think it will cause any such problem. Also, I would suggest you keep a plan B. In case you cannot top up on LTCG, think of any other companies where you would like to invest your amount.
It looks like a good plan! Go forward and sell them to invest in LTCG. Also, since the profits would be quite a handsome amount, I suppose, you should also share the capital and buy some other stocks or a growing company.