Tung Oil Storage

Don't know about Tung Oil but, - - - - for varnish - - - I set the top on one side of the can tilted up and gently breathe into the can several times. This replaces the oxygen in the can with carbon dioxide. Close tightly. I have opened partial cans of varnish one to two years later and just as good as new.

Yes, exhaled air has more CO2 than inhaled, but there's still a lot of oxygen in exhaled air. 

From wiki:

Inhaled air is by volume 78.08% nitrogen, 20.95% oxygen and small amounts of other gasses including argon, carbon dioxide, neon, helium, and hydrogen. The gas exhaled is 4% to 5% by volume of carbon dioxide, about a 100 fold increase over the inhaled amount.

I use Bloxygen in my tung oil containers as it will definitely cure in the bottle. One helpful method of preserving a large container is to pour it into smaller containers and use bloxygen or something similar to eliminate the air in them (I understand that propane and butane will work, since they're heavier than air). That way, you're always working from a small container and if it cures on you, it's less of a loss.

Has anybody tried the collapsible (accordion style) plastic bottles or the 'Stop-Loss' bags?

I've been curious about them but not curious enough to buy them....

I haven't tried them, but I like the concept. However, I doubt that they would be a good long-term storage solution, as flexible plastics have a tendency to allow volatile solvents to evaporate through them and possibly let gasses in or out, as well. It's just a guess, but I suspect they work best with water-based products, like wood glue. If you were varnishing a boat or oiling a paddle and used one of these to store the product between coats (rather than long-term), I imagine that could work well.

If the varnish has formed a hard surface layer - which doesn't always happen - I just lift away the hard layer on the surface and put the varnish through a cone-type paper paint filter, into the 'paint pot' (usually a yogurt container).

We shouldn't ever use the varnish can for a paint pot, right?  :)

The difference/possible difficulty with some of the oils is that they come in narrow-mouth screw-top cans.... but I haven't had problems with hardening with those - yet.

Obviously its oxygen that is the enemy. How about saving in small glass jars like jam comes in. Then fill them to the top. And then the last half filled remaining jar will just suffer the O2 fate - and that's the one you use first. At least you will have some saved for a long time.

In the days before the internet I remember reading stock makers suggesting topping off the open container with stones to displace the air.

Ball bearings or marbles work best for this, as they're not porous and don't contain potential contaminants. They're also easy to clean and reuse.