You're welcome to try but don't be disappointed if you don't get to 5ghz. You'll likely run out of vcore headroom before thermals become the limiting factor. Many like mine do fine with gradual vcore increases until you reach a certain point and then it hits a wall. For me I reach 4.6 at around 1.285v, I managed to get to 4.7 but it took 1.35 to 1.36v. That sizable jump in vcore to get to the next multiplier stably is evidence of hitting that wall where even if temps are in check the vcore required are just too much.
As far as the cooler, the t4 and 212 evo aren't much different. More of a sidegrade since they're so close in price and performance. I don't know what shipping is like to AK, is free shipping or standard shipping not available? An nh-d14 doesn't run much more than a budget aio cooler so if you're considering one, may as well get the nh-d14 (or similar).
Since you're able to get to 4.4 with such a budget cooler it sounds like you got a good chip. Unless you're determined to get another 200-300mhz out of it and invest in a more expensive cooler I'd say you're doing good with what you've got going on. 75c under load during stress testing isn't so bad, typically regular usage loads like gaming and other things won't reach as high as the temps you're getting during a stress test. Meaning you should be around 70c or less during normal use. A more expensive cooler may drop it closer to the low to mid 60's c but will cost 2-3x as much as the tx-4.