Is it possible to get a certified intermediate certificate for your level 2 domain, and be able to certify your own level 3 domains?
May be, you can use a wildcard certificate for your level 2 domain, aka the one valid for any level 3 subdomain of your level 2 domain. Let's Encrypt does offer those (if you can pass DNS challenge). In this case, the only difference is that you are using the same certificate for all subdomains rather than creating individual certificates for each subdomain.