Hello!
I may be able to automate this process by writing a script in iMacros. I should be able to use your list of Gmail accounts and content as a datasource and have the script log in, send an email, log out, and then repeat the process. I can also use proxies to help from getting blocked. How many emails are you trying to send?
Feel free to share some more details with me.
Looking forward to hearing from you!