Nice bp!! Yeah, from the pics I'd say he could definitely move up to a small/adult mouse.
And actually your setup is pretty good. The half log isn't too bad since you put it up against the side of the tank and covered it. The cave hide looks a little too big for him, but if he's been eating it shouldn't be a problem. I would also suggest putting the vines back in though, it would definitely make him feel more secure. You could also cover the back and sides of the tank with black construction paper or cardboard.
Having both an UTH and a heat lamp seems a bit much for the warm side, but as long as your temps and humidity are correct (90-92F warm side, ~80F ambient, 50-60% humidity) then I'd say you're looking good
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