It’s doubtful the salvage yard will give any more with the better rims, but do ask what the car will be worth ‘with’ or ‘without’ them. Some yards are buying the engine and tranny-the rest is gravy for them. I ended up keeping a lot of addons from my 25 year old beater (with the yards knowledge), and sold them on ebay and craigs list later on. Helped soften the blow.
Hunt up your local import club. There are probably guys there who want stuff off your car that might give you more money than you’d get from a salvage yard.
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Since you are REALLY attached to the car, here are some ideas . . .
Do not pay for any more cooling system diagnosis
Remove the cylinder head
Measure the head and block for warpage, if it’s within specs, do NOT send the heat out for machining
Do NOT send the head out for a valve job
replace the head gasket and associated gaskets . . . felpro is fine, even better if it’s cheaper than oem
replace the pressure cap
replace the thermostat
replace the radiator . . . get a cheap one
Do not replace the water pump, idler, tensioner, timing belt, cam- and crank-seals, because you did those last year
Naturally, this doesn’t make economic sense
And if it works, you keep your car, and it’s relegated to backup vehicle
I’m saying this, because clearly you will really miss the Integra, were you to get rid of it
What I’m throwing out there is kind of half-bakes, but the goal would be for you to hang onto your car, and keep it in reasonably good operating condition
Food for thought, FWIW 
I debated posting, but here goes…I did it! Replaced the head gasket. Now I KNOW many of you are going to call me a fool who has parted with her money. Only time will tell and if it’s a costly lesson learned, then I will hang my head in shame. However, it’s no more than some people (not myself though) lose in a weekend at Vega$. Just giving an update in case any previous posters were curious.
Picked it up yesterday and she drives great, as always. The only thing that is different is the sound of the engine. It makes a slight whining sound when the gas peddle is pushed down both in neutral, and then during driving, but not at idle sans depression of gas pedal . YES, I already researched the whining issue on other topic/posts, but was not sure if I should start a new one.
Took car back to the shop after driving it around and mechanic said it’s probably the sound of the new timing belt that I’m not used to. What if the tension is too high? This was stated by a response to another post. If so, I assume they’d have to go back in and loosen it? Bet they won’t like that!
Before I picked car up, one of the techs was topping off the Power steering fluid in an area on far right of engine compartment, right next to the radiator overflow/reservoir tank. There is a belt just to the left, that appears to be “moist” with fluid. Is this the Power steering belt? If it has fluid on it, is this bad? I wondered if it is the source of the noise.
Anyway, Here is what was done to my car.
**Rebuilt cylinder head
**Gasket set (head gasket I assume)
**Timing belt/water pump ( even though they’d been replaced last year…probably should not have been talked into that)
**Distributor cap/rotor
**Radiator
**Thermostat
**Spark plugs, ignition cables
Brake rotor and pads ( needed doing anyway)
Apologies for my lengthy post, esp to @VOLVO_V70. I can’t help it!
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I’d delighted you did. You join the tiny number of people who let us know what happened. Many more happy motoring miles to you.
;-]
Well, fluids shouldn’t be on belts, but are you sure the guy refilling the P/S fluid didn’t just accidentally spill some on the belt?
To be clear, the sound starts when the gas pedal is pushed, but does it continue as long as you’re giving it gas?
Congratulations!
Clearly, you’ve been very happy with the car, all these years
You keep on top of everything, as you’ve just proven, and it will last a long time
Even though this may have not financial sense, it did make sense, in a different way, because the car has sentimental value to you 
Perhaps the accessory drive belt(s) have been overtightened, causing the whining noise . . . ?
This should be easy to determine
I think it is probably the new timing belt that you are hearing, like your shop suggested. It’s still a little stiff. If so it should quiet down w/a couple hundred miles of normal driving. It shouldn’t be getting any worse tho. If it gets noticeably worse, take it back to the shop asap.
I’ll add that I had this exact symptom on my VW Rabbit years ago, and in that case it was the fuel injectors making the noise. There wasn’t anything wrong w/them, it was just that after a repair I was listening carefully for any weird sounds to make sure the repair had been done correctly & I began to notice a sound they had always been making. Whining during acceleration.