DNSimple supports a proprietary URL record type that does an actual HTTP redirect, as opposed to ALIAS, which attempts to look up the IP address of whatever target URL you’ve set as the record’s value. It only works for HTTP/S connections, which is perfect for my use case.
I solved my problem by creating a URL record type that redirects HTTP/S requests from my apex domain to the www subdomain.
More info: DNSimple Redirector - DNSimple Help