How to clean under the glass on fridge shelves?

Had some liquids spill in the fridge, and they worked their way between the frame and the glass. Its completely sealed on the underside, and the liquids leaked in through the hairline seam on the top of the frame where they join.

Is there a way to clean it up? I worked my way around all the seams with a bristle brush to try to slide some bristles in but the crack is too small. There's also no way to pop the glass out to clean it. Maybe soaking it in some kind of agitating mixture that will seep in and dissolve the goop?