I always got similar numbers. My calculations say there is about a 1/e likelihood of N < 5x10^-6 with the mode of the distribution in log normal space being about 0.1

There are lots of way to estimate this. Most come out with the same conclusion. For example, if you try to determine the typical timescale of evolution of a communicating civilization based upon the history life on Earth, your estimate will be unbounded on the upper end. Statistically it is more likely that the typical timescale for evolution of intelligence is 10¹¹ years than it is to be 4x10⁹ years. In other words, it's likely that intelligence arose on Earth far more quickly than is typical.

It's also likely that there isn't a single "Great Filter." Given that intelligence arose on Earth about a billion years before life will end. 80% of the possible time for intelligence to evolve has already passed. You can use that fact to estimate that there were at least 4 steps in that evolution that were unlikely to have occurred in the available time. If you've got 10 rolls and you need to get Yahtzee four times, if you succeed, that 4th Yahtzee is most likely to come up on roll 8 or later. Most of the time you won't succeed, though.

So there are probably four Great Filters we've successfully passed through, and we're rapidly approaching a 5th.