I don't think they exist at your specs and price range.   Did you check Newark, Mouser, Digikey?  Assuming you did, most industrial fans are >12v, thick, loud, and >$50.
 
 

If quality and long life are a consideration then Noctua 200mm fans should work. If you just need airflow then something like the Bitfenix Spectre Pro 200mm is about the highest airflow you'll get.

The Noctua NF-A20-HS ones on Watercool.de are the only 200mm fans I have experience with (1200RPM, ~124CFM, 31dB). Couldn't find any 12V ones on Mouser, Digi-key, etc. Most of them are "round" not square, so the bolt-pattern might be different, and you'd need 24VDC or 48VDC to run them.

So, my idea should work, but would require a bit more cutting than expected, so not going to do it just yet, unless I feel the final build needs it.   What I found was a 200mm 12V radiator fan that can push up to 600cfm!   
 
Shown here next to the Phanteks 200mm case fan that came in my Enthoo Pro case:  

Even the mounting holes are perfectly aligned.  BUT, it's for a car  which is why it has larger mounting holes, but it only cost me $23!  I actually used a 3.7V (4.16V charge at time of test) 18650 battery to power it on for the first time, and it spins up super quiet.  I then put two batteries in series (~8.3V) and tried it.  Still at least as quiet as the 200mm Phantek, but pushing a LOT more air.  But there are 2 strong negatives.....
 
1> the tone of the fan spinning is rather harsh, at 12V it'll probably even worse - I tried to get the tone with my phone but even from about a foot the phone doesn't pick it up. 
2> It's thicker than advertised, It's 2" thick around the outer edge but tapers up to 3" thick in the middle (was listed as 2"), and that presents a problem as I would have to cut away a LOT more of the case than I though I would.  SO for now I'll pass.  
 
The tone thing, I could probably fix by getting a good quality fan instead of the cheapest one I could find, but this was also the thinnest one I could find, the better ones start around 3" & go up to 4" thick.  This would put the fan really close to the GPU.
 
 

SM-71
Shame... I was hoping that someone knew of a brand I hadn't heard of that had something   Guess I'll just stick two of my 140's in there

Hoggle
What are you finding since those CFM are pretty high and better than Noctua 200mm fans are able to do and they are considered one of the best brands for people who want performance from a fan without RGB.

Some of them weren't 200mm - it was getting late & I was missing little details like that lol...
Silverstone Air Penetrator AP184i Pro 180mm - 1,200rpm - 143cfm - 34.5dB - $35+ 
Fractal Design Dynamic X2 PWM GP-18 180mm - 300-1,200rpm - 153cfm - 35.4dB $45+
ThermalTake CL-F015-PL20BL-A 200mm - 800rpm - 130cfm - 28dB - $14+
BitFenix Spectre Pro BFF-LPRO-20025B-RP - 200mm  - 900rpm - 149cfm - 27.5dB - $20+
Yate Loon D22SL-12H - 200mm - 600rpm - 135cfm - 25.5dB - $16+
 
This morning, I'm thinking outside the box a little more, yet still inside the case... I have had outside the case ideas as well, but those wouldn't be very convenient.   Found something that might work, 12V 200-210mm 500-600cfm but no idea on noise, or if it can be run at lower voltage.  I'm sure 500-600cfm is going to be at least 50dB & likely higher....   Will definitely require some case modification, but just might do the trick.
 
No... I'm not going to tell anyone what it is....   unless it doesn't work out.   It it does work, it'll be posted in my next ModRigs post 

I would be more worried about brands I hadn't heard of since often times people will find things well beyond other brands capabilities that are in product descriptions and in the end it's just a knock off cheap product that may or may not even work. It's very common on SSD's to find those kind of products it seems and I am sure case fans also gets them. 

Not sure what he has, I have 3 of these, Noctua NF-A14 iPPC-3000 rpm for front intake. They push 158.5 cfm each at 41 dB, a little loud at full speed but not bothersome to me. 
 

SM-71

fergusonll
Not sure what he has, I have 3 of these, Noctua NF-A14 iPPC-3000 rpm for front intake. They push 158.5 cfm each at 41 dB, a little loud at full speed but not bothersome to me.

 
Same fans, 41dB lol, more like 60dB at 3 feet, but guess that depends on how far away they measure from.   Even with a headset on for gaming, I can hear them at full speed from 6 feet.  
 

That reminds me of the old Delta fans I used to use years ago. They were super loud to the point that I started to care more about getting the noise down while still moving as much air as possible.

Of course gaming headsets have came a long way since that time.

RE: the Noctua NF-A14 iPPC 3000RPM fans.   
 
Out of curiosity, I purchased a RisePro SPL meter & I was darned close....  At 6 feet, with the two Noctua fans at 100% fan speed, it measures the sound pressure level at an average of 61.2 decibels but has a margin of error of +/- 1.5dB.  I did 3 different tests in the span of 30 minutes with MAX readings of 60.8dB, 61.7dB, & 61.1dB.   Measurements with the foam windscreen on the microphone.
 
I looked up Noctua's testing method.... "The sound pressure measurement is carried out according to the following standards:
ISO 3744, ISO 3745, ISO 7779, CNS 8753, JIS 8346
 
The test setup is as follows: The fan in free-flow mode is suspended in vibration-free position at a distance of 1m from the microphone, and the entire setup is located in an anechoic chamber."
 
So while it's cool that they're following pre-set laboratory guidelines... as they also mention: "Installation applications such as on a heat sink or in an enclosure can generate additional noise that cannot be represented in such a measurement."  Which of course means not real-world results due to added vibrations, echo's, & turbulence from being installed inside a case, on a radiator.