Hi Derek. Don't make Mnemonic too focused on mechanics if you don't want to. Brad's idea (or what I managed to understand from the documentary) sounds fine, but it's not exactly what I had in mind from your pitch. Or what you had in mind apparently, based on your conversation with Tim.
I fully agree with Tim (and STG above me): make sure this is the game you want to make. If it's a narrative-driven game, don't let mechanics get in the way of your story. Do think of strong mechanics, but don't make Mnemonic a game strictly about the mechanics. Don't think that because you're not a designer you won't know how to design. Hear everyone's opinion, but lead the project. I'm sure it's going to be an awesome prototype!