Labels would make a fortune if they just set up an online license request store. Any track in various lengths for various prices. Once you pay, you're granted a license. Could take a few minutes for a podcaster to search a song, buy a license for the right length, and you're done. Have a URL that displays a license and instruct creators to put that at the bottom of their video/audio description. Then, any bots can scan for the license URL, verify its key as valid, and move on if the license is valid.
Charge affordable prices (e.g., $1 per second) and make it easy to use. This would take very little time at all and even if it's dirty, the catalog data and mp3s should exist for most stuff. Add a "this track can't be licensed" when data is missing and offer a "let me know" signup.
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