In an effort to track down his estranged girlfriend and reconnect with her, a recovering alcoholic embarks on a cross-country journey that turns out to be poignant discovery into his past.

“track down his estranged girlfriend” = goal
“recovering alcoholic” = protagonist character flaw
Now, “… poignant discovery into his past.”? Would you consider expanding …?

I think of a logline as a short story synopsis, rather than marketing. In essence, a logline contains the spoiler – marketing doesn’t.

If this were my logline, it might read:
When a recovering alcoholic [experiences an inciting incident], he must track down his estranged girlfriend [or suffer some terrible fate (insert story stakes here)], but when he learns of a poignant discovery from his past [state what that is exactly], he must [insert another story goal here], …

Of course, this is your story. What ’cause & effect’ (read: Inciting Incident) motivates our main character toward his story goal (i.e. recover lost girlfriend)? More importantly, what’s the character’s arc? Recovering alcoholic -> transforms into -> altruistic character …!
As a stereotype, alcoholics are usually selfish, self-centered, focusing only on their pain. Consider watching the film Leaving Las Vegas (1995). Slightly different premise, more a tragedy, because our main character never really learns, that love has always been with him – even in his dying (climatic) moments!