I don't see how a cname is relevant, however to the extent it might be there are at least 2 ways to handle this component - by far the easiest is to replace them with an A record. I'm not sure if you realise it but with respect of http/http a DNS record only point to a server - there is no mechanism to manipulate/forward sites within DNS
Unfortunately the answer for the "heavy lifting" component is likely "you can't", but it will depend on the hosting provider and whether you want to do http or https.
For http, if you can get a static IP for only your sites, and if your provider supports it, you can use IP based virtual hosting, which means the webserver will answer the same for all websites which match that IP. Unfortunately, https breaks the above due to certificate negotiation. You will need a way to generate a certificate listing all the hosts being answered for, and keep on updating it. Practically there is no way arroubd thus unless you ignore cert warnings or can create your own CA.
An alternative to the IP based virtual hosting method would be to stick with domain based hosting but programming in all the domains as aliases.