Email Notifications not Going Out

I have about 300 members that need to be notified when there is a new post. Originally I had configured mail as PHP Mail. I am using Easycron to spark delivery by EasyBlog. Using PHP Mail, I was getting the bulk of the notifications delivered, but there were groups of people who did not receive them. My ISP support claimed that PHP Mail was not as reliable as SMTP and they have requested that I move to that technique. Since moving to SMTP nobody is getting mail. ISP folk have tested the link somehow and claim that everything is set up correctly. When there is a new post 300 messages are queued and visable in "email activity". These messages appear to be sent at the rate that I would expect given the parameter setting in EasyBlog and EasyCron. After a couple of hours all are sent. unfortunately I cannot get one user to advise they are received. Help please. Without notifications the site is down.