Yea, this appears to be the idiots at Microsoft causing this issue with the "New" Outlook.com. My account was just converted over.
Seems there has been an issue since December 2015(yes 2015) with the "New and Improved" Outlook.com with sending emails if you use a Connected Account and make that connected account your primary email address(which then uses that email account's sending server). The reason I did this is because I want the "From" address to show as my Home email address, not my Outlook.com address.
There are threads all over the places with people with this sending issue, all the way back to 2015, yet MS continues to not fix the issue, yet continues to convert people's accounts over anyway(it worked fine before the conversion).
The reason I used Outlook.com was it provided PUSH via the iOS mail app, while GMail doesn't. Looks like I am going to have to go back to Airmail/Spark until MS gets this fixed(if ever).