Regarding the 64-bit kernel ...
The short reply - your mac does not support 64-bit kernel due to the 32-bit EFI limitations. More information - Link.
Screenshot taken from - http://support.apple.com/kb/ht3770
The specifics ...
Using terminal to set ... sudo systemsetup -setkernelbootarchitecture x86_64
Details - http://support.apple.com/kb/HT3773
Use of 3rd party software to set 64-bit kernel boot.
Details - http://timesoftware.free.fr/k64enabler/
Thanks for highlighting the specific Mac Pro you are running.My kernel_task (which always has PID 0) says that the kind is "Intel" in the Activity Monitor, but many of the other applications are listed as "Intel (64 bit)". So I have a feeling that I'm not running using the 64 bit kernel. I tried your trick of holding 6 and 4 upon booting (i.e., immediately after I heard the chime at startup). Am I doing something wrong? I feel like a newbie with such a simple question, but I appreciate your help!
Notice that I'm running a former generation of Mac Pro right now, namely, the 667 MHz RAM version from 2007.
The short reply - your mac does not support 64-bit kernel due to the 32-bit EFI limitations. More information - Link.
Screenshot taken from - http://support.apple.com/kb/ht3770
The specifics ...
Using terminal to set ... sudo systemsetup -setkernelbootarchitecture x86_64
Details - http://support.apple.com/kb/HT3773
Use of 3rd party software to set 64-bit kernel boot.
Details - http://timesoftware.free.fr/k64enabler/
Details - Link"... Apple's 64-bit kernel requires both a 64-bit processor (a Core2 Duo or better) and 64-bit EFI."
Details - Link"Specifically, some earlier Core 2 Duo-based Macs have a 32-bit EFI firmware, and despite the fact that a 32-bit EFI can load a 64-bit kernel, Apple (so far) limits these machines from doing so. Ironically, a tool to enable hackintoshes to boot Mac OS X can enable Macs with 32-bit EFI firmware to boot Snow Leopard in 64-bit mode."