Since it goes to your page, you could edit it, then underneath the profile image it should say, edit thumbnail.
You could put your website along the bottom of the profile pic, then the share button would have your url.
You can also make your site's name clickable under your About Section in Facebook. Those are for the visitors that enter through Facebook.
I see you're into video, too. There is a cool optimization channel called VidiSEO you may want to check out if you get a chance.
Great site!
Jared
