Re: Tru-oil
Air in bottom or air in top, doesn't matter. It's usually the air bubble inside that causes it to dry, not leakage around the cap.
That said, the stock bottle and cap aren't great for long term storage; the seal falls apart on the stock lid. Wide-bouthed brown glass containers are better.
Adding marbles to take up the air space is the classic old method for photo chemicals, and it works for other things too.
If your Tru-Oil has thickened, it can be thinned again with mineral spirits. It should be thinned to apply anyhow, even when it's brand new.
If you really can't buy it in Europe, see if you can get Beretta brand Tru-Oil. It's the same stuff, just relabelled.