Have you tried DKIM signing? All email sent from Gmail is DKIM signed,
so they probably also support checking it and a valid signature may
lower your spam score.
DKIM is definitively a must have for gmail.
At least this isn't Hotmail where mail is just silently deleted with no NDR
after it's accepted by their MTAs.
If Hotmail is doing that to your messages, you're in a quite bad
posture. That's their way to tell you "we don't like what you're sending
at all".
Did you consider hiring deliverability consultants? I'm afraid there is
no magical way to reach inbox without a audit of your process and systems.
Benjamin