FWIW I believe you're making this harder on yourself than it needs to be. I can pretty much assure you that your problems will go away if you update boinc to 7.0.36 and update your drivers to 12.11 beta. Uninstall the 12.10 driver and run a program called Driver Sweeper to clean things up then install the 12.11 beta driver. Turning off Aero is that last trick if the first 2 don't work. I've had 0 stuck tasks in 3 days with the above updates.

Got the results:
With a value of '5 minutes' for the 'Turn off the display' setting, the issue of a stuck HCC-GPUv6.56-WUs returned: 9 out of 70 such WUs clocked at 5 to 7 minutes elapsed time with 1 WU clocking 3m46s (when I opened BOINC and clicked on this WU and with that click, the WU got focus and therefore got out of the stuck state) while the remaining 60 clocked under 3minutes.

With the results thus far, the hypothesis now seems to be that:
Setting a value of 'Never' to the 'Turn off the display' Windows-setting may have left the HCC-GPUv6.56-WUs with focus and this focus is needed to have the said WUs not get stuck.

The above hypothesis reconciles nicely with my other observations:
1] A closed BOINC can't possibly supply focus to any WU. The HCC-GPUv6.56-WUs that did not get focus while being crunched gets stuck.
2] When an in-progress HCC-GPUv6.56-WU is highlighted, the act of highlighting forces the focus on the said WU. The said WU does not get stuck.
3] When an in-progress HCC-GPUv6.56-WU does not get attention after 2 to 3 minutes, that WU is likely to get stuck. Why 2 to 3 minutes? Because that's exactly the time my typical HCC-GPUv6.56-WU completes. With every such completed WUs, the focus is gone with that WU. The next HCC-GPUv6.56-WU to execute does not automatically get the focus, and without that focus, the said WU is likely to get stuck.

As a bonus, I have Aero turned on just how I like it! Just have to remember to manually switch off the power to my monitor when I'll be away.
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@andzgrid: Why are you torturing yourself? Wouldn't you rather have a rig that is set and forget with 0 stuck tasks?

Focus has nothing to do with it. Aero has no affect on your ability to crunch either.

All invalids, hung, and errored WUs are caused by corrupted OpenCL package, corrupted driver installs, unstable GPU VRAM (decrease frequency and/or increase voltage to memory here), unstable core (increase core voltage), unstable RAM and/or CPU overclock. If your CPU/RAM is even the slightest bit unstable, it will cause havoc. Make sure all systems undergo intense prime95 and furmark stress testing before unleashing them on BOINC. However, Furmark won't catch the GPU memory errors, so let invalids be an indicator that you need to lower the memory frequency. As well, make sure all equipment is properly cooled, heat is noise, like a microwave power on when you are talking on a cell phone, the more heat, the more likely an error is produced.

What I stated is a hypothesis, not a dogmatic assertion alluding to a possible ultimate truth to which you come out loud and proud to contest. And what makes you so sure that focus has nothing to do with the situation I described? And who said anything about Aero affecting any one's ability to crunch? Ah yes, of course, it was you and only you.
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