Scheme makes no difference here, whether with old or new wording. By the time you discard a card, and then optionally topdeck it with Scheme, it's no longer start of Clean-up, so it's too late to do anything with Walled Village.
But the interesting question is the interaction between Walled Village and Improve. The question is, what does "At the start of Clean-up, if you have this and no more than one other Action card in play" mean, timing-wise?
Let's say you have 3 Action cards in play. Both Walled Village and Improve trigger at the start of Clean-up, so you can choose the order. If you choose WV first, there's no question, you can't topdeck it. But if you choose Improve first, and trash a card, you have 2 Actions in play. Can you topdeck WV now? I would say yes, since it's still technically start of clean-up - you're still in the process of doing "start of clean-up" abilities.
After you've resolved every "start of clean-up" ability, you continue with clean-up, which means discarding cards. Scheme triggers now. As I said, it's no longer start of clean-up. (Scheme v.1 also triggered at start of clean-up, but all you did was choose then.)