Don't write every pixel by hand to the screen. At high resolutions that just won't work. No modern UI does that anymore, they all use acceleration of some type. I ran into this trap when I tried to write a simple canvas game engine.

Just caching blobs of things that don't change frame to frame and got me a 5x-8x speedup, even if where I render those things at changes frame to frame.

Trust me, I learned this pretty quickly. Areas are only queued when the display has to chnage in some way. There's also a bunch of prepratation before drawing a region of the screen; only the objects that appear within the specified bounds are even considered.