My 2 cents.

As an aside - since this was not your fault, is the other company providing alternate transportation for you (e.g. a rental) while this is being resolved? In NC, the law is that they must provide the option... although they tend to keep they're mouth shut about that unless you ask.
Here's why I ask. In general they are in no hurry to settle. You're the one out, not them. However, if they are paying by the day for rental fees, then they are now motivated to get it closed (they're obligation for the rental car ends the day you get a check). This gives you a lot more leverage... you can hold out on THEM until they agree to a price you like (and in the meantime, you get to drive a shin new car). In NC at least, the case is not closed until both parties have agreed.

As for "value" - the problem is in the definition of the word. Value (regarding cars) literally is what somebody is willing to pay for it. Right now the 'value" of Hannah Montana tickets is what, $100 or more... even though the actual cost is about $30 Guys with kids know what I'm talking about... If you can find several ads suggesting that people put a value of $4k on a truck just like yours, great, that defines it how you want. However, the fact that you're having a hard time finding them suggests that, well, the value is less.
What makes it more confusing is that the insurrance company's job is not technically to give you thr value of the vehicle. It is to either repair the damage or replace the vehicle with a similar one. If an agent happened across one in identical condition sitting in a barn, and bought it for $500, they would be within the law to give that to you. On that note, technically if you are a real ass about it, you could make them actually buy the vehicle and deliver it to you. Most people just prefer to get the cash to do it themselves, b/c they either want the $$ to use for something else, or will get a different vehicle.

My vote is with the others here. Get as much as you can. AND still have it totalled out (note if the "value" gets too high, it won't be totalled). Law may be different in WA, but in NC they HAVE to allow you the option of buying it back from them at "salvage rate" - which I believe is 15%. So you get a check for, say, $3k (plus cost of tags, title etc - remember, it's the total "replacement cost"). You then pay them $450 to get it back. Now you have your truck AND $2550. Do the repairs cheaply (even 1k) and set the rest aside for a rainy day. Officially it's compensation for the devaluation of your title - but it's good for a vacation trip too!