Yes, CentOS appears to behave better than Slackware did–at least as far as WordPress is concerned. I was actually able to install a plugin on the new machine. However, I wasn’t real impressed with the WordPress Import plugin–it didn’t appear to do much at all–even after I got it installed. What really made the difference was doing a mysqldump of the wordpress database on the old server, and importing it into this one. Then all the posts showed up like nobody’s business.
All that’s left to be done is to change this server’s internal IP address so that it routes correctly out to the internet. Then I can start looking into installing a different theme and additional plugins.