Thank you, thank you, thank you!
Based on your advice, and the nifty clues about looking at php.ini, I first consulted my PHP Bible (pp. 599-603). There, it points out that the function set_time_limit won't work in safe mode. Don't know if that's of any real concern, because I have save_mode = Off anyway. The author does point out that if the modification isn't working, to stop/restart httpd. I restarted anyway, just to make sure. So now, the php.ini section reads:
max_execution_time = 300
memory_limit = 32M
So far, there are no funny messages about "Fatal error: Allowed memory size of 8388608 bytes exhausted". If it returns, however, I'll revisit this thread and take it up again. Thank you again for pointing in a constructive direction and for providing useful clues.
cheers!