Update: Previously whenever I would get the BkSoD, when I ctrl+alt+del out to Windows desktop, The game had not actually crashed, just hard froze. This time, I got the "Mass Effect(TM) 3 has stopped working" error. I thought I'd post the details in case they help solve this issue.
Problem signature:
Problem Event Name: APPCRASH
Application Name: MassEffect3.exe
Application Version: 1.5.5427.124
Application Timestamp: 50d4cab0
Fault Module Name: MassEffect3.exe
Fault Module Version: 1.5.5427.124
Fault Module Timestamp: 50d4cab0
Exception Code: c0000005
Exception Offset: 0005d227
OS Version: 6.1.7601.2.1.0.256.48
Locale ID: 4105
Additional Information 1: 0a9e
Additional Information 2: 0a9e372d3b4ad19135b953a78882e789
Additional Information 3: 0a9e
Additional Information 4: 0a9e372d3b4ad19135b953a78882e789