yeah, that hole in the new box looks a little funky and difficult to maneuver actually. I'd cut off that top part as well. if you decide to try a new box after this one, though, I recommend just getting one of those black cement mixing tubs at home depot or something. they work great. I have 3 of them! and the smaller one has sides that aren't that high so you shouldn't have to even worry about cutting an opening for him. if he's a big kitty, he should have no problem at all stepping over the side.
and I would not recommend leaving his original one uncleaned, especially if there's no other box for him to use that he likes yet. he might start developing an aversion to using the box properly all together if it's dirty all the time.
putting his used, but clean, litter in the new box is a great idea I think. and maybe put it just a little farther away just to start with. move it closer slowly so he doesn't feel like it's being forced on him.