Ah dear.
Well, removing keys with blu-tack worked great - see the attached photos for what the inside looks like.
I thoroughly dabbed blu-tack all over the underside of the key and the slot, but it didn't change anything.
So now there's two C-shaped stuck out bits that form a sort of X shape. I noticed a lip at the top of one of the C's which I thought might be a mistake from the plastic casting mold and the cause of the stickiness, so.. I scraped it off with a tiny screwdriver. Unfortunately, this hasn't improved the situation a whole lot, at the cost of the key no longer having much resistance to coming off. Derp. I may have to request a replacement key. We'll see how it lasts.
So I'd recommend not scraping off the lip xP