Is it accurate to say:
All HC-110 varients have a very long shelf life as long as the bottle is unopened
Yes.
Is it accurate to say:
An unopened bottle of the viscous (water free) versions probably won't last any longer than the thinner versions?
They tend to last for many, many years - decades in some cases. Thee newer less viscous versions haven't been around long enough to tell whether decades long longevity is a possibility, but its probably unlikely. There seems to be some indication that the newer stuff has very long life when unopened, but there isn't much data.
Is it accurate to say:
Once made into a 1+3 stock solution, the HC-110 developers storage life is no better than many other stock solutions
Yes
I say "might have a longer life" because I still don't know how long we can expect the water-based concentrated developer to last if it is in an opened bottle which is less than full. If it's more than 6 months, then the thin ones would have an advantage over the thick ones, right?
It isn't "water based". It just hasn't had all the water excluded/removed from it.
Is it accurate to say:
Manufacturers of the viscous varients recommend mixing the whole bottle to a 1+3 stock solution when the bottle is opened
yes? no?
The manufacturers make several, complementary recommendations. One of those recommendations is for high volume users - think commercial labs or shared community/school darkrooms or very busy photographers - is to make up a stock solution and then use it quickly. Other recommendations describe how to use it for one roll/tank at a time. The latter is what most of us do, and requires some care and precision, but it is eminently doable. There are a number of approaches to this, including how it is described in J-24.
Is it accurate to say:
If the above is true, then it seems to me a bottle of the thinner HC-110 developer (like Kodak Professional High Concentrate) might have a longer working life than the viscous type (like Ilfotc HC or the new Adox). By "working life" I mean the time between developing the first roll from the bottle and the time when the developer goes bad. Because the thin stuff can be measured to make up only what you need today, the unused portion of the bottle remains concentrated, and therefore retains its undiluted storage life -- unlike the thick stuff that gets diluted to a stock solution on day one.
It is easier to use the thinner stuff one roll/tank at a time. But it isn't all that hard to use the thicker stuff.
Most likely the biggest difference in longevity observable between the versions will be in relation to opened, partially full bottles of the concentrate. The oldest stuff tended to last and last. The newer stuff is likely to be long lasting, but not quite as long. Again, there isn't enough data out there about the newer stuff and multi year usage.