shifting blue pixels

This sounds like a hardware issue. Specifically, either a faulty display, or logicboard. To test, take a screen shot the next time the distortion appears. If the artifacts appear on the screenshot, the problem is most likely related to your logicboard. If they do not, the problem is with the display itself

How should I approach the logicboard issue?

This is a hardware problem, specifically your GPU, and no online troubleshooting will address it. The only way to fix this is to get it physically repaired. You can bring it in to a local Apple Store. I would advise this at the very least, because they will confirm the problem, free of charge, by running a diagnostics test. If a component fails, they will then give you a quote. Out of warranty, a logicboard is a pricey fix.

As an intermediary test, you can use the Apple Hardware Test. Run the extended version, 3X back to back. Note this test will produce false negatives, especially in regards to logicboard related issues.

Using Apple Hardware Test - Support

am backing up via crashplan and considering drive genius 3.... understanding that it may just be a matter of time before it craps out entirely...

This is the best plan of action at this course of time. I would advise against drive genius as a back-up method, as it is not really made for this purpose. I would make a physical backup in addition to crashplan (to my understanding, crash plan is a back-up stored on a server). You can do so via time machine, or software such as Carbon Copy Cloner.

Make an appointment at your local Apple store and confirm the diagnosis. You will then get a price quote and you can decide the best plan from there...sorry to be the bearer of bad news. BOL. Regards.

happy to write that you solved my problem

I wish I could...but, I didn't. These communities are filled with members much more experencied than I...turns the apple "geniuses" into used car salesmen. That being said, they still got the hardware. All jokes aside, it really stinks to have hardware fail, especially when facing the costs Apple charges 😐 . The new Mac Pro should be out soon...always a silver lining [if you have 3k+ to drop and can look at a failing Mac as, rather, a blessing in disguise 😎]. Best of luck.

If this is a Mac Pro 65lb tower, and

They tell you you need a new graphics card, and

They offer to sell you an exact replacement card older than the Apple-firmware 5770, >> PASS.

Buy the 5770 as a minimum, about US$250. It works in all models of Mac Pro, has more VRAM than older cards, and supports OpenCL. Drivers are in 10.6.5 and later.