Ok, I've got a bit of an update. I enabled error logging in the LS php.ini (it was already enabled, but not writing to the web server log, so I had to explicitly specifiy a log file). Once I did, I was able to find the PHP error that Gallery wasn't displaying. It seems the orignal error was caused by the LS PHP module looking in the wrong place for mysql.sock. I corrected that in /opt/lsws/conf/php.ini and am now getting a different Gallery error. Unfortunately, unlike the first one, this one isn't being logged. I've updated the post in the Gallery support forum and am still waiting for any feedback over there.
I think you'll understand when I say that I'd rather avoid compiling a new version of PHP for a single application. I may have to do so eventually in order to get PHP5, but I may just stick with PHP5 via FastCGI (once I have time to figure out how to get that working).