That there's this much ambiguity surrounding what's often called the "Simple Savonius" just seems strange. The terms and formulas should be concrete and anyone using them incorrectly should be easily corrected.
I always figured it by the diameter of the cylinder too but all I know for sure is that that's the prevailing theory.
"I tried to build one without the middle pipe but was never able to get it to stay straight over any length of time."
A design like my "quick vawt" makes that fairly easy. If you want any real power out you'd need to scale that up a ways but that shouldn't be too hard to do if you're determined. I've been considering ordering some custom "U" brackets so I could use larger diameter pipes (in the spirit of "go big or go home") but the only place I've found that'll do short-runs wants like $40ea. for 2 custom brackets. Ouch.
Savs are already less efficient to start with so I never even considered adding a shaft to mine. So far I've been lucky, my barrel-vawt has held its shape fine for the last few months and last week it saw a nice storm so I know it's good to go. My "quick vawts" are just toys (yard art) but they've held their shape just as well.
"... but due to swept area differences it really did not address the real efficiency issue of most power produced in a certain diameter turbine. That means that the less overlap the greater the swept area so the more area to extract power from and it skews(screws) the figures."
I get why they did it that way though; you have a cylinder with whatever diameter, now make the most efficient rotor you can. The diameter of the result doesn't matter so much when you look at it that way.
The most power for a given diameter turbine is a different question that you have to answer (at least in part) with modified blades, different designs, etc.
If you're trying for the most efficient (drag-based) rotor for a given diameter then I think the so-called "squirrel cage" vawts have the edge. The little one I made has a 9in diameter and sweeps 2.88sqft. The closest Sav. I have to that has a 10in diameter and if it was as tall as my squirrel cage it would only sweep 1.62sqft.
The squirrel cage wins by 1.26sqft (!!!) and the squirrel cage is an inch smaller in diameter. That's a fairly drastic difference at that scale. Of course that's not the efficiency difference but it should still give an idea. I don't know how that scales either but I'd imagine the squirrel cage keeps its edge.
And now that I've rambled off-topic, I'm done. I don't care that much to drag this out. Eyeballing the gap and overlap seems to work well enough for me and I probably won't be making many more Savonius rotors anyway. take it easy