The Coffee lake i7's seem to have a tendency to run hot, even at stock configurations. In fact, there is an entire, many page long thread dedicated to that here somewhere (I'll find it and give you a link so you can read up on it) and a bunch of them at other forums too.
Unfortunately, any cooler worth using is going to be at least as large as that 212 EVO, but unlike the EVO, the ones I'd recommend actually work very well. The EVO isn't terrible at cooling either, for a budget cooler, but it's mounting system sucks and more often than not people do not get an adequate amount of mounting pressure when installing the EVO, resulting in poor cooling performance.
I suspect this was probably the case in your situation. I've actually written a tutorial outlining this exact issue with the 212 EVO.
http://www.tomshardware.com/faq/id-2520482/solving-temperature-issues-hyper-212-evo.html
There ARE some lower profile coolers that have better performance than the stock cooler by a pretty good margin, but unfortunately they are still rather large, using a lot of space. Unless you want to use a closed loop water cooled setup, it's an unfortunate fact that if you want good cooling you are going to have to sacrifice some real estate for the cooler. Stock coolers suck, we all know it, and there's nothing to be done about it aside from using a good aftermarket cooler.
Any cooler that doesn't take up much space is going to have performance on par with, or slightly better than, the stock cooler. That makes it a waste of time. Also, the stock cooler is usually louder than an aftermarket cooler, most of the time. Whereas a big 120 or 140mm fan can keep the CPU plenty cool at low to mid load conditions without really needing to increase speed much, the stock cooler has to spin extremely fast almost all the time just to keep the CPU marginally within thermal limits because it uses a small fan and a very small heat sink.
There are fanless heatsinks, but I don't recommend them on any cpu with four or more cores, especially not a gaming or professional work system.
There are a couple of options, many in fact, but a few that I think fit the bill, but you're going to have to accept the fact that if you want decent cooling you're just going to have to live with the idea that you can't use a small cooler.
Using an all-in-one water cooled setup might actually be good for somebody like you because you could mount it in the front, which would eliminate the need to add any fans there, it would keep the motherboard clutter free with no big heatsink to piss you off and make getting to things on the board a PITA, AND you would get very good cooling capability. You might even actually save money going this route because two really good front fans plus a 50 dollar CPU cooler would come to about 100 bucks after taxes.
You can get the ID cooling Frostflow 240L cooler for USD $78.61 on ebay (No worries because ID cooling has US based offices in the event of warranty issues, I know, I checked with our cooling guy Crashman on this previously) with free shipping.
https://www.ebay.com/itm/ID-COOLING-240l-AIO-Water-Cooler-Unique-Comet-tail-LED-Lighting-240mm-Radiator/122356708544?epid=2255308921&hash=item1c7d0734c0:g:1JUAAOSwIRxZerrz
Crashman had this to say about this cooler when he reviewed it last year:
ID-Cooling's Frostflow 240L offers the best full-speed temperature ever achieved on this test system, the best low-speed acoustic efficiency of any closed-loop cooler tested on this system, and the lowest price of any 2x 120mm cooler ever tested on our system. However, while some users prefer integrated fan and pump control, the Frostflow 240L uses motherboard-based controls.
ID-Cooling pushes the value envelope by selling its product directly to customers at the lowest-possible price, undercutting competitors by an average of 22 percent. Fan blades designed to operate efficiently at a fairly low RPM are paired with a medium RPM fan motor, so users are best to leave fan control up to their motherboard. Better performance at a better price make the Frostflow 240L this editor's choice among 2x 120mm closed-loop CPU coolers.
Now, all that being said, I personally am not a big fan of liquid cooling for my own systems. I've installed enough of them for customers though that I'm ok with saying they are terrific in the right circumstances, and definitely LOOK much better than a big old air cooler, but for my personal stuff I'm still using air, at least so far. I think in your circumstance though it might be an option to consider.
If you want to stick with air there are a few recommendations I'd make, and any of these are pretty good, some obviously better than others, and of course these are just recommendations for units within the budget you outlined. There are much better coolers available in the 60-80 dollar range.
PCPartPicker part list /
Price breakdown by merchant
CPU Cooler: Phanteks - PH-TC12DX_BK 68.5 CFM CPU Cooler ($49.99 @ Newegg)
Total: $49.99
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-11-06 23:21 EST-0500
PCPartPicker part list /
Price breakdown by merchant
CPU Cooler: CRYORIG - H5 Universal 65.0 CFM CPU Cooler ($46.89 @ OutletPC)
Total: $46.89
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-11-06 23:29 EST-0500
PCPartPicker part list /
Price breakdown by merchant
CPU Cooler: CRYORIG - H5 Universal 65.0 CFM CPU Cooler ($46.89 @ OutletPC)
Total: $46.89
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-11-06 23:29 EST-0500
This cooler has almost as good of performance and has lower sound levels than the much larger, much more expensive Noctua NH-D15, and has a smaller footprint than most tower coolers with good enough performance to make them worth using.
PCPartPicker part list /
Price breakdown by merchant
CPU Cooler: Thermalright - TRUE Spirit 140 Direct 73.6 CFM CPU Cooler ($44.90 @ Amazon)
Total: $44.90
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-11-06 23:31 EST-0500
For under 40 bucks, this is a great cooler. Cryorig makes excellent quality products as well. All these coolers I've listed are terrific quality though. This is a bit smaller than some of these, with only a 120mm fan though, rather than a 140mm fan, so it also has a slightly smaller overall footprint and is considerably shorter than some of these others.
PCPartPicker part list /
Price breakdown by merchant
CPU Cooler: CRYORIG - H7 49.0 CFM CPU Cooler ($34.89 @ OutletPC)
Total: $34.89
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-11-06 23:37 EST-0500
And this is the lowest priced cooler I EVER recommend, but it still has great performance, especially for a 25 dollar cooler, and it outperforms a LOT of more expensive coolers. It is NOT however, one of the quieter units. With a good, quiet fan installed thoug instead of the one that comes with it, it could be a very good option for about 45 bucks including the cost of the cooler plus a better fan like the Noctua NF-F12 PWM chromax.black.swap
PCPartPicker part list /
Price breakdown by merchant
CPU Cooler: Deepcool - GAMMAXX 400 74.3 CFM CPU Cooler ($18.89 @ OutletPC)
Total: $18.89
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-11-07 00:08 EST-0500