Looking back over the post, I see that I did misunderstand it and I should have gone back over the thread to refresh my memory.
Now I see that your question has already been answered.
You file suit against the driver and get a verdict for the full amount of your claim or you file a bad faith lawsuit against the UIM carrier.
Frankly, you'd have a better result suing the driver because a lawyer will do it on a contingency.
You likely will have to pay for a lawsuit against your UIM carrier because bad faith is very costly and difficult to prove.
PS. Fairness and justice have nothing to do with any of this, it's the contract that counts, and that's already been explained.