When I attempted this method, it was actually a lot easier than I thought.
I simply told the GM that I was curious about resubscribing my account. I told him that I liked some of the new features, like the heirloom and toy tab, but wasn't sure if that alone was enough for me to resub. He then brought up the 10 day free trial and lead me with directions on where to find it in my account page.
I replied saying the button was grayed out.
He then proceeded to give me a password reset, and told me that he would just give the 10 day trial because "game time was buggy" atm. He then told me to wait 30-45 mins for approval. He never once brought up my recent expiration date. If he did, he would have easily noticed that I had already had a previous 10 day trial less than a month ago.
Well, after about an hour, I checked back on my account page to find that, indeed, there was a new 10 day trial added to my account. However, once I logged into the game, everything was still in Starter Edition mode, and I couldn't log into anything over 20.
I had to open ANOTHER live chat. This time I got a different GM and I just told her that my 10 day free trial wasn't working. She also told me that "game time is buggy" right now.. and then "toggled" a couple settings on my account and told me to go check if I could log in the game. It worked.
It's up to you if you want to attempt this. You might be able to get more than 3 days out of it.