Yes, changes to Firefox caused problems! I use some Firefox plug-ins that aren't compatible with current releases (like SQLite Mgr). So I installed Waterfox and use it to run these older Firefox plug-ins. Whether or not Mechanize::Firefox would work with Waterfox, I don't know. It might. A more promising avenue is probably Mechanize::Chrome. I am having trouble getting that critter built so I can't say how well it works or doesn't work.

Update: Default cpan install of version 0.60 hangs on one test. However, Corion helped me and..
cpan CORION/WWW-Mechanize-Chrome-0.61.tar.gz appears to work to force a 0.61 installation. Some test cases don't pass but I don't think that matters. At least installation of the 0.61 version does not "hang" and it gets back to a command prompt.

As another addendum, I don't recommend Waterfox for browsing. I current just use it to run an SQLite tool that I like and know how to use. I've never bothered to fiddle with the command line tool for SQLite. The GUI tool gives the info that I need and I can test out SQL commands. Once I have a working SQLite command, implementing that in Perl code is fairly straightforward - the magic of the Perl DBI!