It seems to me that you could find someone here on SOT to file an exemplified copy of the Tennessee judgment for you in the Alabama county in which the company is domiciled.  I'm not exactly sure if this would work across state lines, but I've seen them in cases where a judgment debtor owns real estate in more than one county.  Of course, this is given with my standard disclaimer that I'm not a lawyer, so you may want to ask an attorney about that.

I'm sure there are many fine Alabama abstractors here who would be willing to walk this into the local courthouse and file it for you.  Any takers?

Regards,
Scott Perry