The 4.4/1,000 data comes from a 2007 report (the most recent available) from the state's Department of Health.
I wouldn't say notably higher. I would simply say it's higher than the national average. But I know you aren't going to let me make your argument for you.

I just don't think that if you walk into Neyland Stadium (circa 2008, so it would actually be full) and think,
Okay... there are 100 more people in here who are divorced than there would be if this were Michigan or Kansas, that isn't a significant number to me (I have no idea what the divorce rate is in Michigan or Kansas. I just threw out a couple of somewhat normal states that are located outside the Bible Belt).
It's all semantics anyway. But your point that us Tennesseans are hardly bastions of the storybook American family is well taken. And that, unfortunately, goes for the rest of the region. I'd be interested to know exactly why that is.
That doesn't change my position of being in favor of legislation like this, though. For all the faults our families have, there's something to be said of these children being placed in stable families. And without data showing how many marriages with adopted children end in divorce, I'm going to assume that those couples who decide they are ready to adopt a child are probably more likely to stay together than those who are having issues with their marriage. It would be hard for me to believe that a couple that isn't fully committed to building a family would go through the extremely costly process of adoption. (And I'm going to research this when I have some more time, but I wonder what the divorce rate is by age group in Tennessee, or if that data is even available? I would surmise that there are a lot more folks married at a young age (18-21) in Bible Belt states like Tennessee than in states like Massachusetts, where the divorce rate is much lower, and I would also wager that those young marriages are statistically more likely to end in divorce than older marriages. That might well explain the divorce statistical divide between the conservative South and the liberal Northeast. Assuming all that to be true, I don't know of any 20 year old couples who have applied for adoption, which leads back to my argument that those couples who are seeking adoption are more stable than our divorce rates might suggest.
So I'm for it. And I don't see it as being related to homosexual parents-to-be. Of course the argument is going to be, and you've already made it, that legislation like this would simply make it harder for abandoned children to be placed into a loving home. But I would submit to this debate that as long as we have American couples who go to China and other foreign nations to adopt children because it's easier or cheaper or there's less of a chance of the birth mother seeking to have legal custody reinstated later in life -- until we're willing to cut through the prohibitive costs and overwhelming red tape involved with adoptions to make it easier for middle class families to adopt children -- we're not too interested to begin with in seeing as many of these children as possible placed into loving homes.