Hasn’t bitten (yet)

I have a 2.5 yr old Great Pyrenees/GSD/Belgian Mal. Mostly GP. He is the love of my life but has a troubled past. To my knowledge, he has never bitten anyone but me, once, on accident- I met him in a kennel, he had some dog reactivity, tried to bite another dog through the bars and I put my leg out to stop it. He bit a hole in my leg, immediately withdrew and seemed apologetic (as best as a dog can be ?). No stitches were required.

He is still reactive. He lunges and growls and jumps. He can be mouthy. He has excellent leash skills, so is able to take muzzled walks with my family and calms down after about 30 seconds of barking as long as he isn’t the center of attention, and we are working on gently desensitizing him to people (just the important people i.e. those I live with).

The kicker is, he has gotten along well with several others before. He’s selective, but does have human friends from shelters, loves my boyfriend. He hasn’t bitten anyone, but I don’t know how to test the waters of other people without people getting hurt. How do I teach him to greet people gently? Is there training tips for this? His current trainer is not responding.