One more thing...

The insurance company may have another concern of raising the value to 4k. If they do so and the veh becomes "repairable", they are then on the hook to repair the vehicle properly and to completion.

IE.. they could get in to the repair, have supplements from the shop, and end up paying 4k for the repair. (not sure if there was a tear down prior to the initial estimate). This is the biggest fear as companies :
1. hate to repair a veh that should have been totalled.
2. do not want the liability of not repairing a veh fully and properly. Hence sometimes it is easier to total a veh vs repair, especially on older veh.

The solution to this:
1. Get the value high enough to not make the veh a total
2. as a concession, agree contractually to a repair amount. Get the veh torn down, contractually agree to a repair amount, so that the ins company is assured that they will not get supplemented to death.

Just another way to keep a clean title on the car if that is what you want, all based on substantiating that the value is high enough to repair vs replace..

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1986 Volvo 240DL - 100k
2002 GMC Envoy - 19k
Sold my Cummins, I've got the fever for a Benz Diesel!