counselor,
I forced myself to suffer through three consecutive relationships with alcoholics... my muscle memory just cringed at the word 'exhausted.' Wow, I know how that feels all the way down to my cells.
I too would consider keeping SR to myself, for my own healing (in fact, that's what I've done). YOUR healing is the one that matters here to you. Your husband needs to find healing for himself, and his presence here can influence your willingness and ability to truly be honest about how you feel, should you find that he's NOT as supportive as you're hoping.
In my experience -- sadly -- that mock-supportiveness lasts until they feel threatened, and then it vanishes so quickly we wonder what hit us. You might consider establishing a rational support system (al-anon, here, counseling) that doesn't have anything to do with him. Just my two cents.
I hope you can find a quiet, restful place inside yourself to make some rational decisions about what's best for the rest of your life.
Hugs to you in this tiring time.