Thanks for forwarding this to me! Well, in my view the seriousness of FP is large in all cosmological models and only weakly dependent on the spatial size of the universe. The reason is, of course, that the Milky Way is, imho, sufficiently large for the paradox to be very serious, even if no other galaxy existed in the universe. Of course, the larger the universe is, the problem does become somewhat more serious, but this is just a pedantic reasoning: in my view the difference between 95% and 99% is really not very important... Thus, from my personal viewpoint ironically (since I was trained as cosmologist, and did my PhD in cosmology), the link of astrobiology and cosmology is very weak one, indeed.
(Of course, if you believe the sort of "rare Earth" arguments of Ward and Brownlee, than it becomes somewhat more important, but I personally don't buy that. Opportunities for life and increase in diversity and disparity are so big even in the history of the Solar System, that it is by far premature, not to mention epistemologically unsound, to speculate that we're unique in any reasonable sense.)
Here are some more of Milan Cirkovic's writings:
On the Importance of SETI for Transhumanism
Contact in Context
The Temporal Aspect of the Drake Equation and SETI