Here's how to go about it. Getting permission to record and sell a cover of a song is about acquiring the above-mentioned mechanical license. HFA is the clearing house for just about every song ever recorded in America. How they became this monumental musical monopoly is, no doubt, a fascinating story of power and greed. Sadly we don't have the space for that sordid tale here.
Results are quick.
There's the song we chose, along with a host of others that have similar titles. Next to the song result is a small disc that, when toggled, highlights which of seven options are available. No album match for our song but we're not looking to buy anyway. But we don't want sheet music either, we want permission. Of course, we also strongly believe in musicians getting compensated for use of their music.