Can't achieve a higher than 1920x1080 on AOC U3477Pqu, powered by late 2011 Macbook pro...?
Your Mac has DisplayPort 1.1, which does not have enough bandwidth for 3440x1440@60Hz (DisplayPort 1.2 on newer Macs can do 3840x2160@60Hz), and a passive DisplayPort to DVI adapter can only do single link DVI, which is not enough for the advertised external resolution of 2560x1600. Apple sells a Mini DisplayPort to Dual-Link DVI Adapter for $99 (it costs more than a passive adapter because of the active circuitry required; it uses a USB connection to power that circuitry). If your monitor has single link DVI, even that won't help you, and even if it helps you, you won't get the full resolution from your Mac on that monitor over DVI or DisplayPort without reducing the refresh rate.

It's conceivable that you could get 3440x1440@30Hz over DisplayPort, but your experience thus far with DisplayPort doesn't bode well for that. Some monitors allow you to choose between DisplayPort 1.1 and DisplayPort 1.2 in the configuration menu (I needed to change that on my first UHD display), but even if your monitor allows that, it's not clear that it would help; aside from the bandwidth issue, there's also the unusual aspect ratio.

I have not found specifications for your monitor which distinguish DisplayPort 1.1 versus 1.2, or single link versus dual link DVI, but the specified maximum resolution and refresh rate strongly suggest DisplayPort 1.2. I have a 3840x2160 display with a dual link DVI input which cannot do its native resolution over DVI; I believe that tops out at 2560x1440 (though I suppose it's possible a different dual link DVI output could improve that).

I recommend DisplayPort 1.2 for your PC's video output, when you build it.