If the index funds don't want to expose the imbalance, they will simply not post buy orders for all the shares they need. They will batch them and only post the next buy order after the previous one has filled. It looks like you are thinking that the index funds MUST trade only at the end of the day on Friday. But trading between Fridays close and Mondays open doesn't guarantee them the inclusion price anymore than buying shares on Thursday or Monday. You still need a willing seller and that seller can go wherever they want to get the price they want. And I don't see how trading in a dark pool in the middle of the night gets them that as liquidity during those hours tends to be very low. The trades still need to be reported before Monday's open.
Market-on-Close (MOC) Orders - IBKR
Unless they are going to use limit orders, they have to place them by 15:55, and can not take them back after.