As I see it, we've got probably 4 options:
1 - ensure you purchase at an extremely competitive price, somewhere in the neighborhood of KBB private party fair to good, for a well maintained car. If the car requires maintenance, adjust price accordingly such that your fully invested price to get the car to "retail" mechanical condition falls near KBB fair/good.
2 - when obtaining an insurance quote, have the insurer provide the "actual cash value" or "fair market value" that they're insuring the car for, or ensure that you're obtaining a full "replacement value" policy. If the values to not agree at that time, adjust accordingly with the corresponding increase in premium, if the company will even do this for you. a corollary here, as dane mentioned, is to definitely obtain a GAP plan in the case that you're heavily financed.
3 - accept moving forward and operating the car at some degree of financial risk
4 - choose not to own a ZHP
The 1st option is largely within our control and just requires you to be diligent in your search...and is probably good advice in the first place.
The 2nd option is something that never really dawned on me to ever do, but given this experience I feel that this may be quite critical for the ZHP.
The 3rd option is probably not the end of the world as the chances of this situation affecting most of us are relatively low in the grand scheme of things.
The 4th option is just heresy.