No idea what the programs you mention are for, but,
The higher the bitrate/quality of the 1080p video, the less noticeable increasing the size to fit a 1440p monitor is going to be. There are no ways around that. Images simply look best displayed natively, if it's 1080p, you want to display it on a 1080p display.
By grainy image quality, what do you mean? If you're referring to older movies, then the grain can't be removed. The grain is literally the detail, it's not added in post (unless for artistic purposes).
All the best!