For what it's worth, I don't use a spoon, I have a fairly sturdy chop-stick (around 5mm in diameter), but I imagine any reasonably sturdy stick like handle would work too. When I tried using something thicker, I would get way too much resistance, plus the chop-stick keeps me from trying to stir too hard.
I also don't start trying to swirl everything from the start. Instead I start by slowly swirling about the top third to get the oil a bit worked in then start dipping the stick down to drive the oil further down. The oil acts a bit like a solvent/lubricant and I find it's a bit easier to stir. The only part that's kind of tricky is getting the really chunkier bits at the very bottom.
After things are stirred, the jar goes right in the fridge to keep things from re-settling.
Hope you find a good solution.