Thanks, I think this may be a valuable direction to pursue.
The error-tracking for multiplication in Fermilab seems like it's probably wrong. But I don't think there's an easy fix, since products of Gaussian distributions aren't Gaussian. Since multiplication is more common than addition in Fermi estimates, you might replace your distributions with log-normals (this is what I do when tracking uncertainty in back-of-the-envelope calculations), but I agree that monte carlo simulations are really the way to go.
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Perhaps 'Fermi estimate' was not the best term to use but I couldn't think of an equally understandable but better one. It could be called simply 'estimate', but I think the important thing here is that its used very similarly to how a Fermi estimate would be (with very high uncertainty of the inputs, and done in a very simple manner). What would you call it? (http://lesswrong.com/lw/h5e/fermi_estimates/).
I like the name it sounds like you may be moving to - "guesstimate".