You've got me thinking ... RAM ... do you have a 4-slot motherboard
with all 4 memory slots populated? If so, this could be related. A lot
of boards have problems with fully populated RAM banks, but AMD-based
ones have always been more notorious for it (as I understand). Could
be that the 64-bit kernel is a little more sensitive to this than the
32-bit. Is your motherboard firmware fully up to date?

Just a thought - might be completely on the wrong track.