I sent my rescue to a 3-week long residency training course when he was that same age, 14 months. It was an epic fail, as in huge waste of money. The dog was just too bonded to me and didn't care to be handled by the trainer. But that's just my experience with a single dog, and they are all different.
The dog has made leaps and bounds overcoming fears and with his social skills over the past year, though, so don't be too discouraged. And it did help him immensely, that he bonded with my Weimaraner while they were boarded together during residency, since she is highly social and outgoing. So much so, that the trainer used the presence of the Weimaraner as Jack's training reward. He didn't care about the chicken, just where's my big sis?? So, it can
help to have a more stable dog set an example. But we didn't get much out of it in the end, really. A $2K sit command, and a GSD who was overjoyed at my return.
You said you've tried private training...did the trainer come to your house and specifically address the issue of going outside?
Maybe a trainer (or even a friend with a balanced dog) willing to visit and bring along another dog would work. If your dog sees the other dog happily going in and out the door, and playing outside, he might get curious enough to venture out himself
There's just something about dogs wanting what other dogs have, hehe, and that includes having fun.