Jamie. What is the width and thickness of the current slab? If this was my project, I would take the pieces in the second to last photo and then fill in between those pieces. Buy a sheet of melamine to make a form and use packing tape to avoid the epoxy sticking to it. You could also use regular ply if you use the packing tape. It also doesn’t hurt to use silicone caulk at the joints. I would think for a kids desk, 18 to 20” in depth is sufficient.
As for the epoxy almost any would work. If you can’t do a deep pour you can always do multiple pours. Just remember to write down your epoxy amounts and the amount of dye you use. Also have a heat gun or a small torch to pop the bubbles. As for brands, TotalBoat, West Systems, Alumilite would all work. I just got an email today from Infinity tools about the line of epoxy they are starting to carry. Another place to look is the Epoxy Resin Store.