Our of curiosity, has this even been looked at in the last 11 months?
If running through Gmail, that is part of the problem as they probably think the email is spam. If running through another service, it can all be marked as transactional with all the DNS settings set correctly and should run through fine. Just need a service that can handle it. SES is an option and so is SendGrid. Yes they cost money but with how much traffic this site gets, it'll still probably be less than $20/mo.