I made some headway on this issue... it's possible to use FogBugz' XML API to get XML Release notes. First you have to get a token, as described here.
Then the shell script can execute a command like this one:
wget -OReleaseNotes.xml 'https://fogbugz.mycompany.com/api.asp?token=the_token_value_from_above_goes_here&cmd=search&q=fixfor:MyMilestone&cols=ixBug,sCategory,sTitle,sReleaseNotes'
I suspect there is a more elegant way to do it, and it would be nice if I could get the data in HTML or ASCII format rather than XML, but this is better than nothing.