2560 x 1440 from DVI to HDMI or from DVI to DisplayPort

[ToastyX]

DVI to DisplayPort doesn't exist as a passive adapter, and the active ones are single-link and don't officially support higher pixel clocks, so that won't work.

DVI to HDMI is technically possible with the patcher (you might need to use the -sl option for single-link), but that's assuming the patcher works with your hardware. I know the patcher works with HD 5000-series and newer GPUs, but I don't know what APUs are supported.

Why not get a cheap older video card instead? Something like the Radeon HD 7850 or GTX 750 should work without tricks.