While writing this posting, Max and I had several discussions about anthropic bias. It left me pretty uncomfortable with the application of it here as well, although I often took the position of defending it during our debates. I strongly relate to your use of the word "mysterious".
A prior that "we are not exceptionally special" seems to work pretty good across lots of beliefs that have occurred throughout history. I feel like that prior works really well but is at odds with the anthropic bias argument.
I'm still haven't resolved whether the anthropic argument is valid here in my own mind. But I share Ben's discomfort.
The Drake parameter R* = The rate of star formation (new stars / year). It is set to LogUniform(1,100), meant to be representative of the Milky Way. I can easily replace that in the model with 2000*LogUniform(1,100) to explore your question. The other Drake parameter that might need some thought is f_c = The fraction of intelligent civilizations that are detectable / contactable. For now, let's not alter this one. The other Drake parameters shouldn't really change, at least assuming they are similar galaxies.
With that change to R*, P(N<1) -- the probability there isn't another in the Virgo cluster, becomes 81% (for the 2nd model version with the t V λ decomposition for f_l, which had previously been 84%). The 1st model version that used a LogNormal for f_l changes from 48.5% to 38%.
The versions that explored a less extreme model of f_l (the rate of abiogenesis) see a much bigger change. For example, when f_l is set to 100%, it changes from 10% for Milky Way to 0.05% for Virgo. The Beta distribution version of f_l goes from 23% to 1%.
Your intuition might be that the prob. of being alone would drop by a factor of 2000, which obviously isn't what happens. What you do see is the distribution for N = # of detectable civilizations (which is a probability dist, not a point prob) shifts right by a factor of 2000. But that doesn't mean the area under N<1 sees that same change.