Tool for tightening toilet seat in tight spot

I have a Pressalit toilet seat on a Villeroy & Boch Carola toilet that is a pain to tighten. The area where the nut is located is very small and I have not been able to get a tool back there to tighten the nut.

The seat comes with a plastic wing nut that slides over the real nut to allow for hand tightening. I unfortunately do not have this tool and am looking for suggestions. Picture of tool with hinge:



Rear view of toilet (I can barely get my hand through these holes):



View of nut (through one of the holes in above picture):

I hated those toilets. If you could get a long pair of needle nose pliers to get that wing nut off and then use a long extension with a socket to get the nut off. I know what your up against.