So, unlikely as it may seem, we appear to have hit an actual bona-fide CPU bug.
https://web.archive.org/web/20130228081435/http://support.amd.com/us/Processor_TechDocs/41322_10h_Rev_Gd.pdf has erratum #721:
721 Processor May Incorrectly Update Stack Pointer
Description
Under a highly specific and detailed set of internal timing conditions, the processor may incorrectly update the stack pointer after a long series of push and/or near-call instructions, or a long series of pop and/or near-return instructions. The processor must be in 64-bit mode for this erratum to occur.
Potential Effect on System
The stack pointer value jumps by a value of approximately 1024, either in the positive or negative direction. This incorrect stack pointer causes unpredictable program or system behavior, usually observed as a program exception or crash (for example, a #GP or #UD).
Suggested Workaround
System software may set MSRC001_1029[0] = 1b.