Is possible that routing to the the GMAIL servers have network delays on Verizon that your old provider didn't have.
I have GMAIL and Thunderbird. Will give it a try to see if I have similar issues.
As a side note, when I google gmail thunderbird smtp, I do see a fair number of posts of people complaining about server timeout.
I understand that your previous setup worked fine, but it does sound as this is not a new issue to Thunderbird. Did you maybe get a recent software update? Or maybe check to see if there are more recent versions that may help alleviate the issue.
If a forum member gives an answer you like, give them the Kudos they deserve. If a member gives you the answer to your question, mark the answer as Accepted Solution so others can see the solution to the problem.