Now I think of it, perhaps some large, loose rocks in the ground would be better for drainage. Can you tell I'm not an expert at this?

Since you've got a sink there, maybe a water slide would help things slide along, or at least the odd blast of water to shift stuff that isn't moving much. You could also give it some sort of vibration, an electric motor (indoors) with a shaft going out that shakes the slide, again to keep things moving.

Or, easier (yay!), maybe a rechargeable cordless drill, low-voltage so safe, doing it. Maybe attach the drill to the slide, and mount an off-centre weight in the chuck. Or whatever. Run the charger wire out to it, again it's all low-voltage so no safety worry. Controls would be from running wires to the drill's power switch (ie the "trigger"), then a switch or two inside the kitchen. 

Dunno if too much water would annoy your mulch pile, but you could dig a bit of drainage under it. Not a real drain, just a bit of piping with holes in it, enough to send the water into the earth. Although it might attract the roots of plants. Perhaps cover a square metre of ground under the mulch pile, with something light-proof, so nothing's gonna grow there, meaning it'd have to be a pretty long root to infest your pipe. Then again, roots take water away anyway, maybe it'd be a solution that looks like a problem...

The sink we have has a hose that pulls out, so it'd be very easy to spray water down the slide with it.  The slide & mulch pile would be outdoors, so it'd already have to be prepped to handle water.  Good ideas, ty!

"I think that one key to a successful idea is making it painless to implement."

True that. :)