Aha x2.

Using this changed the behavior to what I expected:

CGI::initialize_globals;

Info found at, where else:

http://www.perlmonks.org/?node_id=11194

By googling cgi.pm param caching

Note that this seemed to clear the params from the object, as shown by the CGIDebug, but did not affect the "count" parameter.

Thanks for all the help, folks.