Put in the fridge and you have something with the texture of molten tar.
When my wife first came here from the USA, she put my Marmite in the fridge. It took me half an hour to get it out of the jar!
But, the thing to remember is that it is VERY strong flavoured. You spread the merest hint of it on your bread. So the stickiness is not relevant. It should be vapour thin.
Excuse me, off for a sandwich now.
PS you can get it in some places in the USA, but you'll have to hunt somewhat. There's a place in New Hope Pennsylvania (near to my wife's old haunts in NJ) that holds a couple of jars for me, and another in Florida that does the same and also one in Houston. (Can you tell the places I mainly stay at in the USA?). Just setting one up in Boston for my forthcoming trips.