The easiest way to increase overall speed is to increase the time scale (actions -> system -> set time scale), but without knowing a thing about your game it's difficult to say whether or not that's the best way to do it. So you could use a global variable that increases every time you finish a layout, and then depending on what that variable is, you'd set the time scale accordingly.
Then there's the design/ethics issue: is repeating the same levels at a greater speed actually going to make your game better? Is it the sort of game suited for this kind of "progression"? Would you perhaps be better off packing up this game and moving onto a new game, so you can practise other skills?
Another strange thing is what you said - you've completed a game, but you consider yourself a layman? Unless your game is ridiculously simple I can't see that as true. And if it is that simple, perhaps you'd be better off spending more time with it, refining it, adding meaningful features and, at the same time, adding skills to your repertoire.
Sorry for the philosophy lesson, just struck me as something worth discussing, but feel free to ignore everything after the first paragraph if it's none of my business :D