Set root domain record to be a CNAME

Correct, it is a breach of RFC 1034, section 3.6.2, paragraph 3:

... If a CNAME RR is present at a node, no other data should be present; this ensures that the data for a canonical name and its aliases cannot be different. ...

This applies here because the root of your zone must also have SOA and NS records.

Use the DynDNS WebHop service. This is free for their DNS customers.

It allows you to redirect traffic for the second domain to the first one, and not break any RFCs.

The redirect is a 302 (temporary) one, so it may harm some search engine rankings. (I suspect this could also be a problem with CNAME records.) See the above link for more information.