I would think a greeting card would definitely get opened because it looks like.....well......a greeting card and not junk mail.
Send-Out-Cards has a "general business" section of cards that you could include your offer and a link or QR code to your site. I'm not sure of the cost per card, though. But even if it's still higher than regular direct mail letters, yet gets results, I think it would be worth it.
So has anyone tried this?