Your's looks great! I thought initially to try stereoscopic but then recalled autostereograms and thought that might have a better chance of the effect working at this resolution. Your submission does a fantastic job at achieving the stereoscopic effect though, nice work! That's really cool to know that is possible at this resolution.
The noise background was not too difficult on it actually! I already knew that I needed one big rectangle to be 6 tiles wide, and the full height of the screen. That section is then replicated as the base background, then with some groupings shifted (by three pixels to keep in theme) to achieve the 3D effect for the "3". I made I think 12 unique noise tiles by hand, then took those and flipped them, rotated them, and duplicated them in a random assortment to make that initial rectangle. I figured there should be enough repetition that even with the eventual offset of the large "3", I should be alright... and I was! The final tile count is 172 if I recall correctly. Got lucky!