I've skipped most of the replies so I have no idea if anyone has come up with this idea or not, but I understand the need for a timer to stop people using insurance as secondary inventory space.
Why not base the 12 hour timer on when the player actually sees the message? If they are offline this would be 12 hours after they first log in and get the notification, and if they are already online it would just start the countdown immediately. This would mean when you don't log in for 4 days because your wife surprises you with a trip to see her parents out of the country and you aren't prepared enough to have tarkov on your laptop ready to go, you don't miss out on the insurance pickups.
It would also be nice to get the things that were left alone in your backpack/rig back be they insured or not.. ie, you get some loot, someone snipes you from the other end of the map and never bothers to loot you, you die in a bush and no one else sees you, your backpack comes back because of insurance, and its still full of all the nice things you had in there.. Would be interesting in the situation that someone does loot you, then gets killed and the backpack never makes it out of the raid, and you get all the things they looted