Proposition:
Attacking a structure gets split into two rounds:
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Round
Attackers can attack a structure whenever they want. They have 1 hour to apply as much damage as possible, there is no damage cap. In this time period the defenders can repair the structure via normal means (no more auto repair) and attack the attackers. Attackers can also shoot the defenders. Damage will be dealt to shields, armor and hull normally. Whatever damage the attackers apply, the Structure will not explode immediately, but the total damage dealt minus damage repaired will be saved for later. -
Round
This happens later for 1 hour in the timezone the defender chose, (e.g. if the defender chooses 15:00 eve, and the attack happened on 08:00 eve on a astrahus the 2. round will happen the following day on 15:00 eve, for a fortizar the day after that, and for a keepstar the defender can even choose the day of the week). In this round damage is capped to 0, but the structure that is damaged from round 1 can still be repaired with repping modules by the defenders. Attackers and defenders can also shoot each other.
After those two rounds, the total damage after round 1 substracted by the amount of repaired ehp from the second round. If the resulting damage is higher than the structures total hitpoints, it will blow up.
This will not get rid of tidi-inducing situations, but there will be no auto-repair, hence no repair timer that profits from tidi