Couple of points:
A) I was all set to say "yes, the test circuit matches the diagram I gave earlier" when I had a sudden burst of doubt which sent me back to the bench to double check the connections.. turns out, after double checking, that circuit shown in the picture does indeed match the diagram.
B) I know it's frustrating, but you're not alone in the slightest way. This app note by Jim Williams (former staff scientist for Linear Technology and revered analog circuit guru):
http://cds.linear.com/docs/Application% ... an12fa.pdfstarts off with three paragraphs that essentially say, "yeah.. these things are insanely fussy". To quote him:
It is not uncommon in circuits of this type for gates from different manufacturers to produce markedly different circuit operation. In other cases, the circuit works, but is influenced by the status of other gates in the same package. Other circuits seem to prefer certain gate locations within the package.
.. and those are the 'easy' square wave versions.
There are times I'd swear the dam' things can detect brain waves and will stop working if they sense doubt.
mauifan wrote:It certainly makes me feel better to know that you experts struggle with this, too... but at the same time, it is somewhat disheartening to try the things y'all tell me (like mstone's circuit) and still not get it to work.

I know exactly how you feel because I've been there myself.. and not all that long ago, either. Last month I spent two weeks glaring at a bone-simple RC phase shift oscillator that Just Would Not Behave. It was part of a potential kit design, but was so fussy that I shelved the whole project because I can't in good conscience sell people a kit that apparently has to be built during a specific phase of the moon. When I've stopped wanting to throw that particular breadboard through the wall quite so much, I'll go back and try again.
mauifan wrote:Based on everything I have seen in terms of this thread, a square wave is an "overamplified" sine wave that gets clipped...
You're absolutely right about that.
mauifan wrote:so in theory and given that I am using potentiometers to tune my circuit, I should be able to find a gain setting that gives me the sine wave I once saw.
This is the part that could potentially drive you mad.
In practice, every sine wave oscillator that actually works has some amount of clipping. If you're really careful (or really lucky), the amount of clipping can be really small. The closer you get to a pure sine wave, though, the more delicate the circuit's balance becomes.
Clipping represents the amount of energy in the circuit above the absolute minimum necessary to sustain oscillation. A perfect sine wave means zero extra energy, so even the slightest dip (which is guaranteed to happen) will push the circuit below the minimum level, and the oscillation will die out.
Potentiometers, meanwhile, are noisy. There's a lot of stick-and-slip action at the microscopic level when you adjust them. That noise echoes through the oscillator's feedback loop and can produce butterfly/hurricane effects. The best way to adjust pots -- and I'm serious about this -- is to move the knob while the power is off, tap the housing with a pencil a few times, wait a couple of seconds, then turn the power on. It's tedious as all get out, but is much more likely to give you repeatable results.
At the risk of frustrating you further, I can suggest modifications to the circuit I've already suggested, or other circuits that might start up more easily. I do feel like I've been throwing lots of fastballs at your admirably patient head though, and don't want to overload you if you aren't in the mood for more unknowns.
When you void a product warrany, you give up your right to sue the manufacturer if something goes wrong and accept full responsibility for whatever happens next. And then you truly own the product.