You're in PA, so my advice will be especially relevant.
So you're dealing with State Farm, the biggest company in PA and the most stubborn of nearly all of them. Upside is the car is still drivable, so you can drag this out as long as it takes.
First, let me address some of your car-guy-goggles comments: Only you and a handful of other Acura-ites care that it's "all original down to the exhaust". Rare? 98% of the population doesn't care. It's just an old Acura Integra ('94 is a really old car these days) with 148k on it. Who buys these cars? Kids. Kids have no money, so it doesn't help keep prices up. Looks like a rust bubble on the qtr panel, so it's no museum piece. You've got a nice old Honda there, and it's nice that you like it, but the rest of the world simply doesn't care. That thing is old news. Harsh, but the truth.
So, accepting that your car is no Buick GNX, let's move on to the land of reality. Your maintenance work is meaningless and adds no value to a car that old. Everything is market driven. Most people don't know what a timing belt is, so again, on the open market (think Craigslist) none of that matters as far as the value of the car as a whole is concerned. The tires should have been measured for tread depth, and that will factor in slightly on the value, but the car is valued as a whole, meaning that it is assumed in valuing a car that it has 4 tires on it already that are in good condition. New tires only bump up the value incrementally. When people want to keep their new tires off their totaled vehicle, I don't argue with them, because it can be cost effective to pay to swap them around and take the hit for some junk ones if they plan on buying a car that can use the same size.
So, to the valuation. Old stuff is more difficult to value, because there are fewer of them on the road, fewer still change hands, etc. So the data is often lacking. The value does need to reflect comparisons to the same car, so it is not unrealistic to expect them to use only GS-R's. But, same year and very similar mileage also matter. You can't use newer ones; even if it's the same car, it isn't accurate. Mileage can be mathematically adjusted, but IMO if they are within 10-15k miles of the subject it's close enough on something that old. So, finding comparables that are truly identical is the key. And then you have to remember that 'sale price' is not the same as 'retail asking price'. So a car advertised for some silly amount is meaningless if it has no hope of finding a buyer. I like completed eBay auctions for actual proof of what something SELLS for. If you find privately offered cars, if you can contact the seller and get an agreed 'take price' for the car and quote the seller's name and date, that may help, though I've never gone that far. Dealer quotes: are useless in my opinion, but PA has them in the appraiser's law so they are legal. Dealers will tell anyone what they want to hear and frankly don't want their time wasted, so very few will throw out any kind of accurate number. I mean, how likely is it that a Acura dealer is going to give a realistic quote on a car they would normally just toss in the wholesale line to go to auction? But, by PA law, they are considered a fair source.
So, if you can arm yourself with REAL comparables at REAL selling prices, you may be armed well enough to do battle. If you can't get a supervisor to approve the difference, then just take them to the local district justice court, present your evidence, and take what you get. In my personal experience going to these things, the car owner has always won. If not the amount they want, at least half of the 'gap' between what is desired and what is offered. Most district justices will side with the individual vs the big, bad insurance company mostly on personal bias. Sometimes I think it's fair, sometimes I can't believe the audacity. The insurer can always appeal, but it will cost them so much money they normally don't bother.
You can, of course, take whatever you get and retain the car but you'll have to go through PA's stupid salvage title process. While not hard, it's a hassle, and the 'enhanced inspection' will cost you a few bucks. That qtr panel could probably be repaired by a good metal tech, but as an estimator I'd probably write to replace it. Probably cost $1500-$2000 to fix, and I don't think that color is a clearcoat so no blend to the door means a perfect color match is unlikely. But, it is a '94 and not on collector plates, so you have to take what you can get.