I have had no other problems with either the video, nor any more BSOD's. I rolled back the driver, then upgraded past the one that hung my system less than a week later. My system is is not hanging, it's just reporting the Opera error every time I run it.

Unfortunately, the lack of a mini-dump reduces the information available to track down the exact cause. The most fruitful approach then becomes something along the lines of what @zalex108 noted earlier: 'What happened the same day or few days before the problem appeared?' That would include new software installations, updates of existing software (especially video or printer drivers), power failures or other abnormal shutdowns of Windows and/or with apps open, etc. The system's Event Logs can be useful in looking back for errors or warnings that occur just prior to when the problem first appeared.

The most typical causes of a c0000005 access violation include corruption of the registry, Windows security and access settings, malware, failing/faulty RAM, as well as defective apps program code. As you can see, the list is broad which can make suggesting a solution path difficult.

Problem signature:
Problem Event Name: APPCRASH
Application Name: opera_autoupdate.exe
Application Version: 44.0.2510.1218
Application Timestamp: 58ed11a0
Fault Module Name: opera_autoupdate.exe
Fault Module Version: 44.0.2510.1218
Fault Module Timestamp: 58ed11a0
Exception Code: c0000005
Exception Offset: 000000000034be04
OS Version: 6.1.7601.2.1.0.768.3
Locale ID: 1033
Additional Information 1: d274
Additional Information 2: d27450c38dce2934b287b336a30b8098
Additional Information 3: b43c
Additional Information 4: b43c5092e71870d1576a9cd066c3c082

Typically, the most effective method of finding the exact cause is to track down the Windows mini-dump file on the problem system (typically at a location like C:\Windows\Minidump\Minidump.dmp) and get analysis assistance from one of the websites that help users identify specific crash causes from a minidump file. Note, however, that the system must be set up to allow creation of a minidump file in the Control Panel > Systems > Advanced System Settings > Startup and Recovery > Settings > System failure: Write debugging information > Small memory dump (256 KB) > OK. If the system hasn't been set to write a minidump file, set it to do so and then recreate the problem/error.

Problem signature:
Problem Event Name: APPCRASH
Application Name: opera_autoupdate.exe
Application Version: 44.0.2510.1218
Application Timestamp: 58ed11a0
Fault Module Name: opera_autoupdate.exe
Fault Module Version: 44.0.2510.1218
Fault Module Timestamp: 58ed11a0
Exception Code: c0000005
Exception Offset: 000000000034be04
OS Version: 6.1.7601.2.1.0.768.3
Locale ID: 1033
Additional Information 1: d274
Additional Information 2: d27450c38dce2934b287b336a30b8098
Additional Information 3: 175b
Additional Information 4: 175b2eed3af8a1bded503731f096829a

I get the auto-updater error every time I run Opera now.

Problem signature
Problem Event Name: APPCRASH
Application Name: opera_autoupdate.exe
Application Version: 44.0.2510.1218
Application Timestamp: 58ed11a0
Fault Module Name: opera_autoupdate.exe
Fault Module Version: 44.0.2510.1218
Fault Module Timestamp: 58ed11a0
Exception Code: c0000005
Exception Offset: 000000000034be04
OS Version: 10.0.14393.2.0.0.768.101
Locale ID: 2057
Additional Information 1: 4cba
Additional Information 2: 4cbaecd1903e4a805e33512a7be3c36d
Additional Information 3: f569
Additional Information 4: f569d627d8bc0598987dbe86348a300e

Extra information about the problem
Bucket ID: 25ce02eb35f6ab44e892d7447b905b2c (120739393754)

Since when do you receive that error?
What happened the same day or few days before the problem appeared?

Maybe your antivirus is blocking the task?