The field goal on third down is an all time stupid decision when you're down 11.
At the very least you use the 3rd down to take a shot at the endzone from 12 yards away.
Worst case it fails and you cost yourself 5-7 seconds. You were always gonna be up against it driving from roughly your own 40 in 40 seconds with 1 timeout to get a TD, but now you'd have ~35 seconds. Not *that* big a difference.
But if you make it now you also give yourself the big benefit of knowing if you made the 2 point conversion or not. If you make the 2 pt then you know you only need a FG to tie, so you only have to go ~20 yards to get in range. If you fail the 2pt then you know you need a TD to win and need ~60 yards so you can call plays around that.
Kicking the FG first means that you have no way to recover if you fail the 2pt conversion after a TD.
The early FG in that situation only makes sense when it's like 3rd and 25 and it's just better to take the FG than spend time. But it's 3rd and 10 at the 12. You've got like a billion plays in your playbook to get that and there's basically zero risk of the clock running. And even if it does you have a timeout.