It feels like this is more about "how working across timezones fails in practice, for this team".
"From 9-10am, I was often unable to work much because the team was on lunch."
I don't understand why the team being at lunch would cause someone to stop working..
They wont allow a single account to be part of multiple teams. For each client I guess I have to create a new DO account, less than ideal. But still better than before.
Wow I started to read this, then started thinking oh just another "leave me alone while I program" post from 5 years ago.
After reading the comments here I went back and read the complete post. Glad I did. That was a great way to describe how interruptions kill the processes.