First post. I've been trolling for a while but I tend to keep to myself if I can’t add value to the conversation and I don’t have an NSX...
However, I was a very good Rep at Progressive for the last few years (which led to my current cushy state job) and I can say that the info here is mostly correct. Most auto polices do have exclusions for first party DV claims through the collision portion of your policy. As this person is underinsured (has insurance but not enough) you may be able to use under/uninsured motorist property damage (UMPD) coverage on your policy, that usually has a reduced deductible and NO exclusion on DV.
Obviously policies vary by state, but it would be pretty easy to read your policy contract (ask your agent if you don’t have one), just look under the UMPD section at the exclusions. UMPD is an optional coverage so you first have to make sure you have though. Then read if it covers both uninsured AND underinsured damages, as it may only cover uninsured damage. If this UMPD coverage does not apply, then you may unfortunately be SOL.
Geico will only pay back there minimum limits with a property damage release from your insurance saying that you/your insurance will not pursue the Geico insured for additional property damage payments. In order for you to get DV from Geico, your insurance would have to sign off on the release stating they are accepting the limits less your DV settlement (i.e. if you got 2k DV, your insurance would only get 8k of the Geico limits). As your insurance company is for profit, I wouldn't bet on them being ok with that (as there already losing thousands in money paid to fix your truck) but it’s a management decision so always worth a try.
You could pursue the at fault party through small claims, as they are legally responsible for all damage above there limits, but from my experience people rolling around with minimum limits have nothing of value, and could care less if there is a judgment against them, so that might not be worth the hassle. Your Insurance co. would likely do an asset check on them, but again, unless they see something of substantial value, they'll likely write off all unreimbursed cots as a business loss.
As for what to submit, all the advice is good. From my experience, which is likely quite similar to Geico (Progressive is 4th largest auto carrier, Geico is 3rd, and both share a similar business model) you will submit your DV documents (Jon Boy’s recommendations were all solid). A rep will give them to a Branch manager, and he will look ONLY at the year and value of you truck, and wing a response like 1-4k. You would think this stuff is reviewed, but usually not. They'll make you jump through hoops hoping you'll go away, but at the end of the day, they will pull a number out there buns. If I were you, I'd go for 10% of the vehicles value. A salvage title can typically reduce 25-50%, so its reasonable depreciation given your car will have an accident, but not a salvage title. That being said if you start at 10% they’ll negotiate down from there, so maybe start at fifteen for wiggle room...
Hope this all helped. Good luck.