I wouldn't say a thing about "rebuilding trust" at this point. It's been what, four weeks now? Frankly, *I* wouldn't trust him at this point. I think to thank him for working to rebuild trust is (a) premature, (b) comes off like a pat on the head for being a good boy.
I know you want to be supportive. Just show appreciation for what he DOES--don't put it in terms of how it relates to his drinking. He's a person, not a lab specimen that you're trying to nurture.
I get the feeling that you're weighing everything you do and say in terms of how it will affect him--positive, negative; help him stay sober, make him drink. That isn't necessary. What you do won't keep him from drinking or make him drink. Just keep doing the "next right thing" as best you can, and you'll be fine.