I've really appreciated the responses so far, as many of them have made me reconsider some things.
That said, I have a new proposition. I'm taking the emergency fund of the table and letting it be what it should be: an emergency fund.
What if instead I sent my biweekly (every 2 weeks) paycheck to a "holding" fund. Within that holding fund, I would have a trailing limit order to buy a broad market ETF if the market dropped, say, 2.5% (I'm playing around with different percentages based on how frequently they happen). If within those 2 weeks it didn't drop, then I simply invest it all at the end of the 2 weeks, in time to replenish the "holding" fund with my next paycheck. This way, at worst I'm keeping money out of the market for 2 weeks, and at best I'll be able to get that particular investment chunk at a slightly decreased price. I admit this is trying to capitalize on small market fluctuations, but it's also basically dollar cost averaging with a 2 week lag time.
Does this make sense? Does anyone know of any long term research into whether this would yield slightly higher returns?