First, I want to publicly commend the level of badassity in this post. The long commute, the right attitude about doing the math, and a willingness to build your own mountain bike frame, together, put most of the people on this board to shame. I'll never read another post that says "I don't want to bike the five miles to work because I might get sweaty" without thinking of this.
Second, I would suggest swapping out your tires on the road bike. Depending on what kind of brakes you have, it may be a simple matter to buy a second hand mountain bike that's not in working condition, take the wheels and tires off it and put them on your road bike. You might even salvage the brakes to make the swap easier. Add some fenders and the right clothing and you're all set.
With that said, if you really want to build a mountain bike don't let us stop you. Using the numbers you quoted, you only need to ride to work 52 days to save in fuel the cost of the new bike. That's less than one winter. It's not as frugal as modifying your current ride, but since you're clearly a serious bike commuter I would personally justify the expense.