In case this is useful information for T-mobile people working on the problem, I did think of something that might be of value.
My system sends email to the <number>@tmomail.net through a python script.
The day before my emails started getting through properly, I was messing around with the computer which was sending the emails-to-sms which were not getting through. I sent a lot of emails from the command line(sendmail) with and without TLS security. Some were getting through in a short time, but not immediately. The next day, my script was sending emails, and they were getting through normally.
Not sure if there's any cause/effect there, but I remember a lot of finicky things about TLS when I first set up the system.
