N00b needing help with 12V LED strips

Your project is calling for custom made boards to be quite honest. As you discovered, both products use large, through hole components, which will ultimately end up in a bulky setup. You can get mosfets capable of switching 1A that aren't that big in an SMD package, but you may have to design the circuitry yourself. Not that hard to do. And at that point, you may as well build a custom board that has a 328P Atmel on it, with the various signals needed for your project, including the mosfets. From your description it doesn't sound like you need a whole lot from the Atmel, so you can eliminate quite a bit from a stock Arduino board when designing your own custom one. The only issue now is that you don't want to have to design your own ... that's a hurdle for you to jump over.