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For some reason my input display program wasn't registering mouse inputs, but the important thing to notice is that you need to wait a little bit after jumping before you start shooting at a dummy to allow your weapon spread to reset, or you will waste time missing shots due to artificial inaccuracy. Using the deagle for 3 kills will also save you a small amount of time, since you move faster with the deagle than you do with the M4A1. You also run faster with your knife, so it's best to keep that equipped any time you're not throwing ammo or killing dummies. Also, crouching while in midair to help you clear certain obstacles you have to jump over is worth it. Your score won't be penalized as long as you spend less than 1 second crouching, so just be careful not to do it too much.
hope seeing a run with the inputs helps someone out though, good luck.
There's a full run of it with my inputs displayed onscreen.