It accepts my personal mail server just fine. You need to support encryption, spf, and dkim but mail will flow no problem to gmail users in my experience.
And yet, most (but not all) new gmail recipients will not see my emails until they remove them from their spam folder.
Google does not want people to self-provide email and there is no incentive for them to do so.
http://www.backscatterer.org/?ip=69.43.165.11
I suggest fixing your SMTP server configuration [1][2] and maybe listing your IP on dnswl.org. (edit: I see you did the latter.)
[1]: http://www.backscatterer.org/index.php?target=bounces
[2]: https://web.archive.org/web/20140215064312/http://spamlinks....
However I was speaking of my own, personal mailserver, which is not listed.
Also - do we really think "big email" (like google) are using either of these (blacklist or whitelist) services ?