Hello Andrew, it seems you have tried different troubleshooting steps and ran some diagnostics. I have few other suggestions:
http://support.microsoft.com/kb/228753 Troubleshooting "Stop 0x00000077" or "KERNEL_STACK_INPAGE_ERROR"
Hopefully any of these will help. I wonder if the Intel® SSD worked properly for some time in the past or if this is a new build or upgrade. Also, is it possible to replicate the issue by copying a large amount of files or in any other way?
Intel® SSD Toolbox is the only software we recommend for our drives.
Perhaps you can try disconnecting the secondary drive just in order to try narrowing the issue further.
Another option is a secure erase, but you will probably want to leave it as last option since it implies backing up and reinstall everything.
A BIOS update may help too.