I'm not familiar with the pixel proportions of modern TVs, but if the problem as you say is truly one of the TV not mapping an input pixel to a screen pixel in a 1:1 ratio as you said, then I doubt there is anything you can do. If you want to test this assumption, I'd say you need to do two things: first, find the resolution you TV claims to be displaying at 720p (which should probably be 1280x720, but you should definitely make sure), then make a PNG at that exact resolution with a checkerboard pattern of alternating pixels (I actually found one just with Google image search at this resolution
here) and display that on your TV. Then get up close and see if any pixels are blending.
I'm not sure if your TV is actually the problem but I think it's important to rule it out if it's not.