I am a licensed agent for a better, more reputable company who shall remain unnamed.
Progressive is not a company that I hold in high esteem for many reasons. In my dealings with them, it seems to be a common practice for them to low-ball settlements for their customers or deny claims altogether based on obscure clauses or limits that are unique to their policies. They also record losses against clients the minute they mention it on the phone ... regardless of whether or not they choose to turn in the claim and seek a payment. While technically "legal" in most states, it's a really lousy way to do business in my opinion.
If I had an accident, I would not want to have them as my company. I also wouldn't want to be hit by someone that had Progressive without having full coverage of my own (so that I could go under my insurance and let my company's lawyers duke it out with Progressive in the background).
All that being said, I unfortunately don't see the proposed settlement as actually being all that low. If anything, it was on the high end of the similar cars that I was able to find (nationwide). What Progressive is looking for - and what you should look for - are comparable cars in the vicinity of where you live. The insurance company is only required to pay you the "Actual Cash Value" of your car before it was totaled. KBB is entirely irrelevant as that is nothing more that some random company's opinion of the value of your car. What counts is what real people are actually paying for similar cars in your area. Actual Cash Value. If it's a rare car (like a 6-speed Kizashi), they should give you a bigger radius to find similar cars, but the pricing of a car in California can be 20% different than one in Iowa... so closer is generally considered more accurate.
If you can provide Progressive with some current listings that demonstrate cars similar to yours are being sold for more than they are offering, you definitely have a shot at increasing the settlement. If you had added anything custom to the car (Stereo, subwoofer, wheels, etc) you can ask for that equipment to be factored in as well. You certainly don't have to accept what they initially offer, but based on the numbers I saw (quick search of CarGurus, Autotrader, and Cars.com), I wouldn't expect to get a lot more (and almost certainly not $8000). Frankly, the AWD CVT comparisons may be helping you... the manuals (though more desirable to a person like me) seem to be selling for about $1000 less...
Last bit of advice, if you have a good agent, you should be talking to them. A good agent will be there to help you and advocate for you with the company. A big part of my day is talking to adjusters and underwriters to be sure that my policyholders get the all coverage that they paid for. If you purchased online to save yourself a couple bucks or have a crummy agent... then sorry. I do wish you the best of luck, and I'm sorry to hear about the passing of your Kizashi.
Oh - out of curiosity, did the airbags all deploy? The Kizashi has like 8 airbags that generally run $2,000 a piece... so for a majority of them on the road, an airbag deployment wreck = totaled.