Thanks for the pictures. I had a totally wrong idea of what was going on. In thought there was a horizontal gap under the substrate. Boy was I offI was thinking of ways to fix this: First, you have the fill-in idea like you were talking about. I actually don't know how well that will work.
My own ideas deal with the depth of the container. If you are up for it, you can cut the bin down or buy a new bin. My girlfriend suggested using a plastic litter box for cats instead. You might even look into how much it would cost to have a custom bin made by a place like TAP plastics, since I have heard they make custom plastic stuff, even weird stuff like props for costuming(The example being an odd shaped sword from an anime.) for a reasonable price. I figure since figure since they'll make a weirdly curved sword shaped peice of plastic with a hole through the middle, a simple dish/tray should be pretty easy...I actually may look into them myself soon for a dish for my African Bullfrog. They might even be able to make one side ramped lol. I've also seen some shallower plastic bins, but most are only slightly less deep. I'll keep trying to think of some way(s) to help solve this. Good luck!