How to forward e-mail to Gmail using a personal domain name?

Gandi is Route 53'a back-end registrar, but that is not a factor, here.

Mail can't be forwarded simply by DNS settings. You can set where servers on the Internet will try to deliver the mail (MX records in DNS) but unless the specified mail servers are expecting email for your domain, it will be rejected. (With Google Apps, you essentially configure the gmail mail exchangers to expect mail for your domain, and that's why it works.)

An alternative would be to set up an EC2 instance with a mail server daemon like exim, postfix, or sendmail, to accept mail for your domain and then redeliver it to gmail, with the original envelope header changed to your Gmail address, but this will defeat some of Gmail's spam filtering, since the mail will appear to have come from your machine's IP address instead of the original sending server. You will need to use TLS to deliver the messages to gmail or request that Amazon remove the port 25 outbound throttling on your instance's elastic IP.

You'd have the same problem of spam filtering being somewhat altered with any mail forwarding service, except that it's mitigated to some extent by the mail forwarding service's spam filter implementation.

Those are the three options, though: configure gmail to expect mail for your domain (using Apps, afaik, is the only way to do this), accept rewrite and forward yourself, or use a 3rd party service.

Recommendations of a specific product or service for email forwarding are off-topic for Stack Overflow. The suggestion of exim/postfix/sendmail is not intended as a recommendation, but merely as examples of common mail daemons shipped with Linux distros.