Any news on this ?
I know not directed to me specifically, but I did try mail.baby. I am having issues with deliverability to Microsoft hosted email like hotmail, Outlook, Office365. They have made some changes which have helped. Still testing.
I recently started testing smtp2go also, and seems to work fine with outlook at least (which is always a pain). 
A client who’s website I looked after for a while used SMTP2GO - always seemed to work well other the odd time their system got a little sensitive and blocked a lot of notifications. But that’s probably better than the other way round.
smtp2go seems to get emails delivered reliably, and when I have needed support they are very fast. At work we use them for about 35,000 emails a month. Services like Microsoft, Yahoo, etc seem to be sensitive to DKIM and smtp2go has a CNAME record to put in your DNS that helps with that.