Then congratulations because you have read it wrong. Adding CNAME records for verification never makes your domain work.
Adding A records do, and changing the authoritive nameservers do. In fact, once you have set the domain up, you do not need any kind of verification anymore and I can say that you’ve wasted your time setting up those CNAMEs.
I would just suggest that keep ZoHo as well as the namecheap NS. Just add the appropriate A records in namecheap and it will do.
The guide below is written specifically for Cloudflare, but most of it can also be applied to other DNS services.